アプセス?OKOKSoOK, soI'll start.So far, I talked about some...SoYesterday, orZip-SawThis is overdifferentchemical species.So this is kind of averageyeahovercells.So this abundances abundances of chemicalsfor instance messenger RNA.So that is somewhat power law behavior.And that is often appear in statistical physics as a transition point.And alsofor cell-cell fluctuationvariancewe have seenlognormal distributionand thenwe discussed some kind of kind of reproduction of cellsand what the nature of reproduction of the cells.And thenI discussed some kind of sleeping state.Actually, this is also shownin this othertalk in this kind ofsowhen you put this bacteria intokind of in new entrainresource condition, nutrient conditioninitially takes some timeand then exponential growsthe number grows exponentiallyand then comes toso they cannot grow anymore.And then finally it goes down.And then the question I discussed yesterdayso how this kind of sleeping stateappears.And thenthen Idiscuss this kind of model.So basically this is a kind ofactive protein.So thatso this isautocatalytic.autocatalytic means that this numberincreases by itself.So for instanceso this increases byproportional to this itself.So that givesusual exponential law.So this kind of behaviorexponential law.And then how it sleeps.So that's the question.And then we consideranotherdifferent molecule species.Andthat is some kind oferrorfrom the original.So this does not have functionto catalyze others.Soand so in some sense if this is largerthis growth is suppressed.And thenif you have some kind ofcomplex between A and Bthen consider such model.And thenif this nutrient islower this fraction is increasedand thisfraction increased.And then it goes to this kind ofyes sleeping state.So the growth ratefor examplethis growth ratehow this increasesthisshowsfromthis growth ratechanges fromthis growth rate muandthis musogoes downat some point drastically.So this is10-9or something.So this is almost zero.So it goes down.So the cell cannot grow.And thenyeah.So we have seenthis behavior.So that meanswithin this nutrient rangeso the cellcannot grow.Or it does not die.So this muis nearly zero.So the reason for that is thatso active moleculeisso trapped by this complex.And so thatwhen it's trapped by this complexso catalyticactivity cannot work.So it cannot grow.So this is so far a model.And we are not completelysure if this is really true or not.But there are some discussioneven in the present cellthere is some kind of such inhibitorfor the growth.And so that may work as B.So probablythis kind of basic ideamay be okay.Of course in biological detailsthere are much morecomplex nature.But probablythis kind of behavior exists.So that'sactually so hereit's trapped by thisactive molecule AA is this one.So active one is trappedby this inhibitorso Bor erroneous onebad one or something like that.Sothis isand anotherinteresting pointis thatokay in experimentso this isso when these cells put into astubbed condition there is no nutrient.So the growth rateso goes downto nearly to zero.And actually one can measurein thisso just lookingat this microscopeand or someplate or something.So this cell stopsthe growthwithout nutrientand stays there.Sometimes they form a kindof strange form or something like thatbut they stay there.And then theyagain put nutrientand theoriginalpicture of thisthis lag phase meansthat when youput nutrientto recover the growthit needs some time.So that's a kindof common nature.So even though youhave put nutrientsit'sfinally this becomes positivethis becomes positiveand it can grow.But it takes some timeto recover thatand actually this issomewhat rather large.And another interestingpoint.So thislag timebefore thisit's okaybefore it recovers the growthand then itstarts to growagain.So hereand this isthe lag.And actually in this experimentor in most experimentsso they put into the starved conditionand how long itis put into the starved condition.So maybeso thisso they put a kind ofso here they start nutrient.And before thatokay no nutrientsometimestarved time.So withoutyeahwith nutrient it grows thisand they cut thisand they are going to this state.And how long itis put to this starved condition.And interestinglythe experiment showsthatthislag timehere it's put lambdalag timeandstarved timethis lag timeincreaseswith the starved time.So this is some experiment.So how long itis starvedand thisis lag time.So in somesense cells rememberhow long I'mstarved.So this is a bitkind of interesting behaviorbecause if this starved conditionis a given justsingle statethenmaybethis lag time isindependent of thehow long I'm starved.If I'monly one bad stateif I'm starved stateif I reach hereit's a single statethenyou need same time to recoverthe growth.But the experiment showsthatsomehowthis lag timeincreases with thisstarved time.So if I'm starved very verylong timeit needs more timeto recover.So that meansmaybe slowly in this starved conditionslow change occurs.And if it goes slowlyto a much worse statethen you need more timeto recover.So that kindofexperimental resultisknown.And howit depends onthis dependence of this and thisthis increaseswith this.Solamda increases of T starvedsomehow increasesmaybe.How it increasesthis dependence is not maybeyet soaccuratelyobtainingexperiments.But anywayincreasing function.Andsome data show thatthis is roughlysquare root ofstarved time.But some experiment showsmaybe it's almost linearof the starved time or somethinglike that.So thatthat point is not yet so clear.But maybe something like that.And actuallyin this simulationwehave seenkind of this kind of square rootin this simple model.Andthe basic mechanism thatit showssuch kind of dependence isso as I saya andb.Soactive one andb.Soit'sslowly this part is increasing.And active one isyehdecreasing.Andin thismodel basicallyb is produced by a.Sowith the aid of a.Soroughly speakingincreaseofbad oneisproportional to a.But a plus bsee.Andat some stage this complexreaches some value.Thenseesome seesproportionalto a,b.Andthat meanssomething like that.This is a kind ofrough estimate.Of course in the simulationwe show this behavior.Sowe try to understand why this kindof square root appears.And so assuming thatthis process is rather fastand it's equilibrated and thisis roughly constant valuethen this.Andthen so wehave this.Sothat meansthat meansb increasessquare root t.Soif you have starvedsothe amount of bis roughlyproportional to t starved.The fraction of bbad one increases with thissquare root t.Andthen tochange the growth.Firstthis is attached to this.Soif you put a nutrientagainthenthis a start to workmaybe this becomesdetached anda starts to be activeagain.Andthen the time neededfor this isproportional to this.Soin this argumentroughly we have this.This is a kind ofrough estimate.But anywaywe have seenthat kind of behavior here.Andmaybe the otherone isthere are other interestingpoints,but maybe Iskip that.Andsorry,I have a question about the experiment.Soall the experiments are done wherethe nutrient supplied beforeand after starvationis the same.Yeahsame nutrient and soit grows and thencut and thenwait sometime.Andthenactually there isthis is theaverage starvation time.Averagelag time.Andactually for each cellsome cell can wake upearlier.And some cansleep longer.Sothere is a ratheryeah,long taileddistribution for this.Soeach cell lag time.Andthis is also,thisprote is something like this.Soandactually if we doa stochastic model for thiswe can have this kind oflong tailed behavior.Andbutfor such experimentyou need to measure asingle cell.Sothat's not so easy.Andactually tomorrowYuichi Wakamoto will talk abouthis beautifulexperimental technique tosee such behaviors.Yeah.Okay.Maybe if you're interested indynamical systemsand thissleeping statefixed pointis somethingso you have twonull clients.Andif it goes there.Andso if it goes tofinally approach,itgoes to thisfinal sleeping statefixed point.Thesetwo null clients are almostin parallel or tangential.Soit takes very long timeto go there.Sothat's this time.Soso relaxation toover this process in thisstabation condition isanyway very very slow.Theslow,the reasonwhy it's slow is thatanyway A isthe active one.Andeverything in this cellis processedby this catalytic molecule.Andthis catalytic molecule number isvery small.Theneverything is slow.Soeverything is slowed down.Sothat's how this kind ofprocess occurs.And if you areinterested in dynamical systems,maybe youcan see two null clientsand how these are.And if you'reinterested in,please refer tothis original paper.Yeah.Okay.So there are some otherinteresting issues in the origin ofrelated to the origin of life.ButI guess I don't havetime to go into detailsto each topic.IfI do this,I needmaybe two or threelectures for this.Andso I'll skipthis.Butmaybe I justsay the topics.So oneis whywithin each cellthere are so manydiverse components.Andactually in this modelor the modelI talked yesterday,justone active molecule,oneactive catalyticspecies.And that producesitself.Andto grow,maybethat is simplest and maybeit works much better.Because othersdo notnecessary,not so necessary.Sobut stillin our cellthere are so manymany components.Maybejust for the growththis will not be souseful.Sothat's a kind ofvery basic question.Andso there are manypossible answers,maybein a different environmental condition.Ormaybeyeahin aif this resourceis limited,then it's better to havemore diverse chemicals orsomething like that.Sothat's one problemand we are discussing.Andwe discussed thatokay,thisbasic start point is thatthese components arein this membrane.Andthis is compartmentalized.Sothe originof this such kind ofcompartmentalization.Thatis a kind ofverybasic issue.Andanotherimportant issue is thatalways.Soin thisorigin of life,information moleculeand functionenzyme moleculeis separated.Soprotein works as thisand DNAworks as this.Andso this mutually helps each other.Sothat structurethat is also known inCentral Dogma.Sowhy this exists oris this a kind ofessential oralwaysuniversal naturefor a cell system.Sothat's also a kind ofvery fundamental question.Andwe discussed somekind of model for thisthatby symmetry breakingthis role separationoccurs.Butthis is stilljust onepossible solution and maybewe are notyet in this final answer.Sothat's we needsome kind of coherent theoryfor these kind of things.Andso maybe I'llskip this.And if you'reinterested in this otherslides listed there.Somaybe you can read thisoriginal paperor you can cometo discuss to me.Andactually maybeI just want to say onepoint here.Thiskind ofbehavior.Justsay a little bit.Maybe Iat least thiswhy theythis kind ofcompartmentalizationisnecessary or goodisokay.Thisproblem.Youhave catalytic molecule.Andthenit's mutuallycatalytic.Sofor thisXI growsto XIsome J moleculeis necessary.Sothis is catalyst.Sothey have some kind ofcatalytic activityKJ.So thisKJ.Soif KJ is large.Sothis catalytic activityis large.Sothe molecule helpthe growth of othersreplication of others.Butthat is good for others.Butit's why I'mworking as a catalystfor others.I'mnot replicated.Sofor eachmolecule's sakedecreasingthis catalytic activityshould bebetter.Soif you consider thisfitness or some growth ratefor each moleculethenfor each moleculeit's betterto decrease this catalyticactivity.Andso I'm alwayssoreplicatedby the help of others.Thatwould be better.Soif you just consider somereplicating molecules set of hereand then mutuallycatalyzing and then catalyticactivity can changethrough evolution orthen probablyevery moleculestarts to lose the catalyticactivity.SorryI did not understand one thing.Sowhen you say that it starts to lose the catalytic activity means thatit's advantage forJ not to catalyze the reaction.Soyeahthis yeahit's mutually catalyzing.Sothis I catalyzedthis other molecule.Yeahbut the assumption here is then that somehowthere is a constraint to the total number ofso that molecules are competing forsome finitepull of resources so thatthe total amount ofmaybe yeah,finite resources.Yeahbut as timegoes onit's usually better to losethis decrease the catalyticactivity.And actuallyif we dothe simulation of thisok,some model took,somutually help thisok maybe.Sorryyeah.I don'tget this.Soessentially selectionselection of each molecule.Yes.Selectionaxa at the level of the whole cell.ok,so that'sthe point.Herebeforeif cell does not existand then justmolecules there.Thenfor the selectionof each moleculethey lose catalyticactivity.Sothat's a problem.Wethis system cannot continuethe growth.Sothen,as Mate alreadymentioned,if these cellsareput into ayeah cellsome kindof.And thenthe catalytic onethese catalytic moleculeshere.So of coursefor each moleculereplicationthey may goto the direction to decreasethis catalytic activity.Butif everything does thatthenas this cell.Sofor instance,if every molecule losesthis catalytic activity.Thiscell,as a cellthiscannot grow.Sofinally this cell dies.Butif you consider the situationthatok,maybeyou havethe numberof moleculesnot solarge.So probablysome cellsthey havethey keep some kindof catalytic moleculehere.Butfor some other cellsthey lose all this.Sothenthese cellsremain to grow.Andthese cellsdie out.So basicallyin this case initiallythe selection works of moleculesbut nowif we go to the cell levelthis selection works as a cellthenthose cellsthat somehow keep the catalytic activityremains.Sothat's howmaybethis is not taken bythis non-catalyticmolecules.Yes.I have a question because I thinkthis is the core of the chicken egg problem.Soyes.Yes.Sothis just exists.Soexactly.So the questionwhat I don't understand the question isgiventhat a cell exists.Thatis possible to have a cell.So that 12 compartmentswhat isadvantages?Is this the question?Orthe question is why it'sadvantages to have cell compartments?That's the good answer.OK.If you have compartmentsof this structurethis can remain.Butmaybeotherwiseif you have justbigthis kind of special structurethen maybe they will finally die out.Sosomehowin thissomeplacethey have some kind ofcell.Soinitially maybe not cell.Butif you have some kind of smallholes.And thenwithin this only enmoleculeshere.And thenif you compete with thissmall structureof these holes.Thenthis guy can grow.So the question isyeah.OK.Yeah.Sokeep in the structure.Yeah.Sothenmaybe it's importantif n in this moleculein the cell.The numbern is too largemaybe they finally losecatholic activity.But if n is notso large.Yeah.There isyeah.So thiscan keep this structure.Andactually yeah.Wesome simple modelwe have a transitionto this kindof yeah.GrowingandOK.Nongrowing.If n isso OK.This isn.And m is thekind of mutation rate.Sothis is how thiscatholic activity for eachmolecule changes.OK.Istill don't understand theselection acting on themolecular level.Becausethere are two aspectsthat I don't understand.One isthatwhat is thiscompetition.Whereis this coming from.Because it's amolecule.It's essentially a proteinand it's doing its job.Andthe second thing that I don't understandishow does it sensethis competition.Becausea cell is a collective structure.Ithas the ability tosense competition andmodify its DNA orhave a mutation tospecifically modify themolecules which make itfitter.Butwhen I'm thinking ofa specific single moleculeI don't know how it sensesthe competition and where is thatcompetition even coming from.OK.Sofirst this moleculeso moleculereplicate.Andif thisgrow this replication rateso it's higherthen this moleculedominate.So iffor example a moleculeand b molecule and a moleculegrowreplicate per 10 minutesand this moleculereplicateby 1 minute,then this numberdominate.Andso for instanceif a and b mutually catalyticand ifa hashigher catalytic activitythen alwaysa is helping the replicationof b.Butb has no catalyticactivity thenb grows this ab does not help a.Soby that b increasesmore and a increasesvery little thenb dominates.Sothat's the molecular levelselection.Andthen the cell levelselection is thatput these kind of moleculesin a cell.So it's a veryprimitive cell.You don't needto consider DNA or anything.So put these.AndthenOK.If such bdominated cellsOK.Initiallythey start tosome a moleculeexist.Butb is dominant.So finallymostly this isb.Sothen thisthe total number cannot increases.Butif you keepsome cells happened towith some fluctuationhappened to keep amore.Thenthis number increases.Andfor instanceassuming this total numberof molecules increases,thenaccording to these cell devicethen these cellscan divide.Sothere is some kind ofsomolecule levelselection and cell levelselection.Andonce you make cell.Sothere is cell level selectionappears.And the interestingpoint is that cell levelselection and molecule levelselection may go intodifferent direction.Soin a molecule levelselection may go intodecrease K.Butin the cell levelselection may beaverage K overthis within the cell shouldincrease or keep some value.Sothat's in a differentdirection.Yes.SoI mean it'sit's right tounderstand thisin the sense thatwhen you think about moleculestalking about proteinsthat essentiallyare subject to mutationso thatessentially you losecatalytic activity.Yeah.Okay.Yeah.Sosothen mayben is important.Andthen how K changesso pereach replication.Somaybe the rate of losingK.Somaybe K itself changesgoing up or down randomlyby mutation.But maybeas a result K decreases.Butthis is some kind ofmutation ratemutation ratechange rate of KM.So basicallyyou have two parameters.Thenumber of molecules in a celland mutation rate M.Andthen the resultsays that suggests thatokay if n is smallerthey can't survive.Butif n is largerfinally every moleculeloses catalytic activity and dies.Andso this is thephase diagram.So this isthe kind ofsurviving region.So ifn is small,okay.Soforget about this Sthis is some kind ofselection pressure or something.Soanyway,sofor instance this,yeahifn is smallerthen you cansurvive.Sothat's some kind ofimportance of this multilevelselection process.Sothey,soand that isimportant whyso K compartmentalizationor cell structureisnecessary.It's good.I'm sure it'snot sure.Butanyway,so this is,yeah.But is this quitehow to say intuitivethat the,so if Ithink about this nand the state ofthe moleculeas some kind of alignmentprocess.Soifn try to maximizethe K,thebehave in the same way,right.Soas a connectiveincrease nrequirehigh selection pressure for allalign.Decrease nit easier for them to align.Increasingincreasing n means thatmaybe,so basicallyifn is largeso in thiskind of multilevelselection and this isone,so which iswhich property is importantfor molecular levelmoleculeor cell.Andfor moleculefitnessK activity goes downand cell levelaverage K increases.But this is average.Soif this is all of Kloses that,this should decrease.Andifn is largethisifn issmallso beforeeach molecule losesthis catalytic activitycell device.Socell's importance is morerelevant.Sothis kind of structure.Yeah.Andactually this kind ofproblem isquitemaybe general inmany system.Youhave multilevel system.Sofor example,if you considera company andI do not work.I do not workbut somebody other works then the companyso can beokay.Thenso butif this total numberis small,then everybodyhas to work ormaybe.Thenso howthis kind of parasitemolecular parasiteworkerdisappears.Depends oris not dominant.Depends onthat kind of total number.Yeah.Sosois there anotherway of seeing what you are saying.Sothat essentiallyso the typicalvalue of K decreases.Butbecause you have anexponential increasing populationthen there isa large deviationof small moleculeswhich have a largeRHK.Yeah.Andthese are those that aredominating growth.It's abalance.Yeah.This is atouch balance.Yeah.Actuallywe can do some kind ofsome calculation to showthis kind of where thetransitional occurs or something like that.Yeah.But maybe.Yeah.Idon't know.Soanyway this isunimportant.Maybegeneral important problemhere.Then.Yeah.Okay.Sothat's one exampleand then.Okay.MaybeI'll skip this.Okay.Then.But thenmaybe you cannotmake a very large cell.So only thisif n is largeeverythingso this molecule,this cellreproduction does not work.Andthen we discussthat when n is largemaybesymmetry breaking that onegroup of moleculesloses this catalytic activityand they workas a kind of informationmolecule like DNA.Butother type of moleculesremain to workand keep catalytic activityso like protein.Soif that is the casesoif n islarge maybeat some point there issymmetry breaking thatfunction molecule andinformation molecule issplitted.Sothat is theorigin of central dogma.Soproteinworks as enzymeand helps the growthand DNAworks asinformation carrier.Andactually that kind of structuremaybeseems to bequite commonas long as you have multilevelstructure.Soin this case I discusscell versus moleculebut in our bodythere is multicellarso this is multicellar organism.Soin our body casewe haveour bodytotal multicellar organismbut you have many cellsand in this caseagainsome cellworks as a kindof information carrier.Sointhis in our case of spermand egg cellcan bethiswork as ainformation transferfor the next generation.But othercells of our bodyso this skinor all otherscannot leave the offspringfor the next generation.Sothat structureso one type of moleculecellsworks askind of information groupand most othersare kind of function.Sothat is quite commonto here.Yes.Asfar as I understandyou said DNA worksas information cellsand proteins works asfunction cells.AndI don't have any sense ofwhat is information cells.Does it mean as the history ofthat you said that they don't havecatalic activity.Doesit mean it is the history ofthe cell.That isyou know I don't have anyidea of what does it meaninformation.I see.I should have explained that.What it refers to.Okay.Soin this case sothank you.So maybeyou have learned the central dogmaand so from DNAinformationnow proteins are produced.Catalysedby protein.Sobasically fromthis informationeveryother.Sofor example this DNAand from this DNAproteins are produced.Andthen DNA is replicated.Andthen from thisyeah proteins areproduced.Soprotein cannotproduceby this information from this.Sofor exampleyou have amino acid sequence.Sothat is kind of information.Butit cannotbe transferred.Onlythis you haveDNA sequence.Andfrom this each DNA sequence.Andfrom this some amino acidis produced.Someamino acid produced.Andthen proteins produced.Soalways proteins producedfrom the information ofDNA sequence.Sothat's the informationI mean.Is itokay.It works as a pattern.Itworks as a formula.Youemphasize ontransmission,theinformation.Transmission to this.Yeah.The sake of theinformation.Yeah.Yes.Yeah.Yes.Andactually so alsoin our cellso this our body.Sookayfor instance each skin cell.Butthat is produced from thisoriginalyeah egg cell.Andthen from this informationthis is made fromthis.Buteven if I have this skinthis skin cannotbe transferred tomy offspring.Onlyyeah egg cellor sperm cellproduces the next offspring.Theinformation is transferred only throughthat.Sothat's a quite general nature.Sothat's a veryinteresting issue.Andso wediscuss some kind of model forthat,but it's still quiteopen.Yeah.Sojust to see if I understand the claim.Sothe claim is that if you have areplicating molecule where the informationis stored in the structure itselfthen if there are mutationsthat advantage the moleculeover the cell this replicatesover generations.Whileif you splitthe information content whichis stored in let's say DNAand the molecule that replicatesif you have a mutationin DNA that corresponds to a largerreplication rate of the moleculethat produces a disadvantage for the celltherefore that will notreplicate.Sobasically by decouplingthese,the information spreads onlyvia the oldpopulation of molecules.Yeah.Actuallyokay.Soin this discussionokay,this modelis too complicated.SoI don't want to discuss.Okay.Sobasicallyeach more,soin this discussion of this symmetrybreaking,sothis catalytic activity Kand thenthe property hasto transfer the informationas template informationso thissome kind of property Kand initiallyI assume that K andP are sameamong all moleculesand if you consider two typesof molecule,one types of moleculegoes here and work.Soas I saidthere is general tendencyit goes to okay.Thereis general tendency to goK goes to 0.But actually some typeof,one typeof moleculeinitially losesK.Thenthe other type of moleculekeeps Kandas a kind of function moleculeworks as a kind of functionof molecule.Sothis kind of symmetrybreakingoccurred in some model.Yeah.Sothis is a little bit.Yeah.Themodel is a little bit too complicated.SoI do not go into details.Yeah.Justsee if I have understood likewe needlike the meanKto raisebecause otherwise this cell doesn'treplicate.Yeah.MeanKshould belarger.Larger.Yeah.Butbut each Ktries to decrease.Go down.Thenme it's justaverage of each K.Soit'sconcrete.Someone goes down and they areinformation one and some.Yeah.Sorry.When does thissymmetrybreaking occur?Okay.Okay.This is a little bit.Yeah.Soin thisstudy as N is larger than some threshold.Yeah.Thissymmetrybreaking occurs.Sobut I am afraid that Ito explain that it's a little bit more details.Soit's so you can seethe paper byTakeuchi and myself.And alsomaybe I have other slides to explain that.Soif you are interested maybe I canyeah discuss later.Okay.Sosorry for this.Yeah.InitiallyI thought I should skip this part butmaybe it's yeah.Becauseit's this kind of structure seems to be quiteuniversal.Soin a kind of multilevel systemso molecule cellor cell-to-multicell organism one groupworks as a function and the other group has a kind of informationtranslation to the next generation.Andusually the function parthas a large number.Sofor example in our body onlyyeah just egg or sperm cellit's a very minority.And most othersyeah muscle says all others are majority.Andalso in a cellDNA is usually one or two or somethingvery few number.And proteins are largenumber.So that kind of structureseems to be common.And alsoin a higher levelSo for instance queenbe or queen aunt.So there is auntsociety.In the aunt societyonly the queen produces the nextoffspring.And all the other aunts areworkers.So again this is functionand information groupand information group is very minorityfunction group is majority.Andmaybe this appears when aunt is largeso maybe aunt has many manynumbers.So then the transition occursI don't know human beingsdo not have enough such number tomake such symmetry breaking so thatyeah we can produceoffspring.Everybody can produceoffspring basically.OkayOkay soyeah I thought I just talked this partonly 20 minutes and butyeah.And I go totoday's number fouryeah today's Thursday alreadyso I go to that switch to thattoday's topicOkay so far we discussed the reproductionand can I ask a question about the previous claimso one I mean could wonder whetherit was I mean it's a game chicken egg but it was bornthe membrane before so the compartmentsor the separation between informationand because you could imagine to have these holesand already of these holes at the moment where there is like this sort of group selectionit might become advantageous tolike the separation between the symmetry breaking between informationyeah but maybe at someor maybe initially there is some kind of membrane moleculesin the very beginning I don't know yeahor even withoutmembrane maybe there is some kind of other wayto make these molecules in a compartmentso that isnobody knows yeah soI go to the topic of adaptationsobesides reproductionso adaptation isuniversal feature common to biological systemsand when we say adaptationbasically there are twokind of different aspectsone is that okayso basically adaptation is thatmaybe this biological systemis put to new environmentand we often say okayif we go into a high temperature regionmaybe some kind of biological state of ourschange so that we can adapt to ahigh temperature region or high altitude regionor something like that so thento adapt to that something should changeso that's one aspectso some changes so that thisbiological system can survive wellin this new condition so that'sokay I start fromchange to a fitter state, higher survivabilityand so thisand another aspectis that eventhis change occurs butmost of the cellar stateor most of the variables in our statedo not change so muchor stay at the same levelor come back to the same levelso this is also another natureand actually even if youput this into a kind of different temperature conditionour body temperature remains within a certain rangeand there are many studiesby physiology studiesthen that is studied by the famousphysiologist Canon andthey he called homeostasisso many biological stateremains at the same levelso of course if you put to thisnew environment initially this change occursbut finally most of the variablescome back to the originalso these arekind of two different aspectsthis say changebutmostlydo not change so there aretwo aspectand actuallymaybe this is kind of verybasic issue in biological systemand this is sometimes this is calledplasticity so this can changeand this is called robustnessit does not change so muchso how these two are compromisedthat's the basic issueso in this today's lectureso I discussedfirst changeabilityhow this is changedok so nowthe standard pictureof thisadaptabilityto change to a new conditionis that there is some kindof cell signaling so weput this bacteria into a new conditionand then some changein this internal state occursand standard pictureis that there is some kind ofok externalso we have this nutrientbut we do not have this nutrientor something like thatimformation so external informationcomes into the celland maybe some kind of membraneor something base sense and then cell signalsome signaling process signaling networkthat has been discussedin or investigatedin detail and then leadsto some kind of this changeto gene expressionso that means you have to produceproduce proteinthis protein Aor protein Bor something like thatso for instancein this conditionyou have to produce protein B instead of protein Bso this is the process thatso from this DNAok you have the region to produce Aor B and thenthere is this signal transduction networksays some informationthat in this condition you produce Aor but in the other conditionyou produces Bso there is some informationso that's kind of general picturethat isim not saying that this is notcorrect ok this works inmany examplesmany biologists checked aboutthis kind of cell signaling networkand how this kind of structure in some conditionhow this process occurs and this issometimes very complicated but theyfind outso that'sthat's ok so maybe this cell signalingnetwork can be evolvedafter so many generations soif this bacteria put into this condition okI have to produce protein A otherwiseI cannot survive thenmaybe if some cells findsome kind of specific network then they can surviveand then evolvebut still one question is thatbacteria can survivein various conditionsand sometimes experimenters doput this bacteria into a quite strange conditionthat recently produced environmentso we have many recentlyfound some kind of some chemicalsin somethe kids from the factory or something like thatthen they put this bacteriathey still many times they still can survivebut then it's hard toimagine they have alreadysome kind of historyfor the evolution to survive this and they inventsome cell signalingtransduction networkso they prepareall many differentpossible environmental condition and they preparedifferent cell signal transduction networkhow this can be possibleso that'sa question hereso that means adaptation to a huge variety of environmentsso the question issignal transduction networks are preparedfor all of theseand this may be a little bit hard to imagineso if there is some generaladaptation mechanism that may not beso sufficient as the signal transduction networkin the case of signal transduction networkif you put this new environmentimmediately they start to produce aand all of these cells can survivebut is there some other mechanismthat may be not so efficientbut at least they can work more generallyif that kind of thing existsthat would be quite goodactually there are some experimental suggestionsthat they put thisfor instance this is Elisha Brownin Israelso they did some kind of put thiseast cell into a different conditionand they somehow surviveso the question is that is theresome mechanismthere is kind of change of gene expression dynamicsto switch to a kind ofbetter survivable conditioneven without kind ofdirect external informationso that's the questionactuallyso is there any generalmay be primitive mechanismabout twenty years agoso a colleaguemine worked outsome constructive experimentwhat they did is something like thisin this bacteriathey put some genesand they cut out some other genesbut they put these genesand so basicallyin this as shown in this figurethere are two sets of genesand there is promoterso from this gene starts to beso transcribedso this set is transcribedso there is two setsgreen and redand thenwhat they put is thatwhen this cellwhen these genes are producedtranscribedthey generate these proteinsso this is hereso in one case, Lacquan GFPGutamin A,Gutaminaseand this is a red fluorescent proteinthat is for Abut the name is not so importantI do not know so muchso biologists should know what these names meansbut maybe for physicists the structure is importantso what they have hereis thatwhen this genethis protein is producedthis suppresses this otherand when this is producedthis suppresses otherand that one structureand the other structure is thatwhen this is producedthis make green fluorescent proteinthis is for measurementif this is expressedwe can see this is greenthe other thing is that this is producedthis is redand another thing is thatthey produce some glutaminaseand this is for A or somethingand that isnecessary for the growth in one conditionso here later we put these cellsinto a different conditionso this is necessary for survivalfor other environmental conditionthis is necessaryso maybe for simplicityyou can call this maybe red conditionand green conditionso this is glutaminasesome condition or somethingbut for thisthis is necessaryso the question hereis thatthis isso we put this gene artificially producedso there is no wayinformationso if there is some kind of signal networkthen this is in a green conditionyou can make this green proteinso if some signal transaction network existswe can do thatbut this is put into hereso there is not such structure hereand then can they knowwhich state is expressedand first of allI have to say why this kind of structurewe putso I did not talkin this geneintroduction to dynamical systemsbut basically twoset of genes suppresses each otherand x1, x2and when x1 is expressedx3 is suppressedx2 is expressed, x1 is suppressedand that meansm1, m2and from this protein2 is producedand protein1 is producedthenso you have heard thisheal coefficientin the other lectureand for instancehere we take the case of this heal coefficient2so and this is suppressingso that meansas written therem1is producedwith some ratebut if the other guy existsit's suppressedso for instance like thisand this is something like thisno no no protein2can be different between the twobut for simplicitywe can take this symmetric caseand then from thatokaymaybe degrade itdegrade itand then from m1you can produce p1p1.m1m1-p1and of course you can put some coefficientsbut for simplicityI put this coefficient1and thenso basically you have this equationand then you already heardthat okay in a messenger RNA processyou can do much fasterthen you canideabatically eliminate the messenger RNA variableassuming thatso this goes to the steady state fasterthen this goes to thisand then you solve thisthis equals 0and put this herethen you get this equation herestandard2variabledynamical systemand thenso you need to solve thisbut most of youhave alreadynew about dynamical systemsso if you have this equationthen what you need to first dois to get new clientnew client means that the conditionin this caseso in this dynamical systemsyou have p1p2variableand this dynamical system shows thatokay where it goes here in fixed point or something like thatand then new clientis that p1.equal 0this should be 0so that is one new client is that p1and the other is something like thatsince the model here is symmetricso it crosses at p1 equals p2so you have a new client of thisand okayone new client is thisand the other is something like thisso okay basically thisand if you have new clientso maybe you learned dynamical systemsso you can check thatin which direction the flow goesso above thatso above thatso this goes todown this direction is downand this goes upso right or leftand up or down is changed by thisso maybe as a homeworkyou should write down thisand then check what kind of structureis in this dynamical systemsand write the flow of thisso at each point you can consider p1.p2.and that gives this flowand by writing down thisstructureyou can understandwhere finally this dynamical systems go toand thenso you can see this structureso basically there are three crossing pointsand in this crossing pointsboth are satisfiedthis is a fixed pointand there are two types of fixed pointsone is herethis is fixed point p1.equal 0and p2.equal 0so this arrow goes out along this directionso if you part up a little bitit goes this or thisso that means this is unstableso unless you veryput exactly on this pointit can be therebut any small perturbationcan kick the state to go outso this physically does not existthis fixed point cannot be reachedand on the other hand these twoare kind of stable fixed pointsso this is naturalbecause mutually this is suppressingso either this guy winsso this guy winsand the other guyis almost 0so p1 is much larger than p2or p2 much larger than p1so that means green winsso the kind of these cellshave mostly thisand thenokin these dynamical systemsyou can have both possibilityand maybe if you start fromhere it goes here it goes hereand if you have some kind of noisemaybe it goes here it goes here equallyso the first questionwe addressed hereis that okay dynamical systemsthis butfor a cellif this is expressed in one conditionit can survivebut for the otherif it goes to the other stateit cannot surviveif you put these cells into this conditionmaybe half cells go herehalf cells go here and half can surviveor half do not surviveand they do this experimentand put thisso here so without glutamine environmentand for that they need to be greenmaybe this is green oneand so without glutaminethey have to produce glutamine by themselvesso they need glutaminaseand then it's better to go thereand if the cell goes through thisit shows greenmost cells go to greenso this is a real experimentand for the other casemost it goes to redso now the questionif there issignal transaction network to say thisokay you have to go to green this is naturalbut in this experimentsuch signal transaction networkwas not put so then why isthat this possiblethat challenge to theoryokay maybemaybe if you are suspiciousokay even though we said that there is nosignal transaction network put into thismaybe somehow hiddenthere might existit's very hard to imagine but maybeusually some referees in thepapers would ask okayif that might exist or something like thatokay to check that they didthis promoter genesso that is the initial partthey start this so express genesand if there is a signal transaction networkthis gives informationto thisif there is a hidden transaction networkif you swap this in this experimentand make promoter of this promoter herethis promoter herethen it'sgo to a different statethen maybe hiddensignal transaction network to go to greenbut then it goes to now this other sideand then it should not workbut actually even though they change thisstill it worksso that meansthis hiddensignal transaction networkhypothesis is not possibleso the question is thatokay you have this kind of structureby stable structurebut somehowmechanism that good fix point isselectedgood means that cell can grow fasterso okaythis is hidden hypothesis isdeniedand okaymaybeI can start this simple casein this caseone missing point is that cell growsand as cell growsit's dilutedand if it's dilutedthen to balance thisthe synthesis increasesso instead of this initialdynamical systemswe have this p1there's thisthis is growth rateactuallyso minus mu g x1is dilutionby the cell growthmu g is the cell growthso this is always thisto balance thatthe synthesis is always probablyhigher okaywe discuss this point laterbut anyway thisand then similarly thisnow you consider this dynamical systemsand maybe mu gdepending on the condition maybein green cell this is mu g'slarger green state green conditionand this is smallerso mu g may depend on herebut still this is just overallfactor so that meansmaybe this is largethis is small but still this is fixed pointand this is so if in some conditionif this condition is better okaymu g is large and mu g is smallbut still this is just a factorso basically you have thisstable fixed points hereso only by that nothing changesthen butall these processes are stochasticso you put some noise herethat's reasonable to noisewe can seethat kind ofswitching to a good state occursand that is somehow expectedbecause both are stable fixed pointsbut since with thisso with this condition green conditionthis mu g is much largermu g so this kind ofthis fixed pointgreen fixed point is largerthan mu g red conditionso this is quite smalland this is quite largeand then if you put some noiseand then maybe by noise it can be easily kicked awaybut this isattracting much morethen we may expect that okayby considering this growthdilution and balanceplus noisethen we may expect thatattraction to a good state occursand with this simulation of this modelthisand in changing the environmental conditionin environmental onegreen condition has alarge mu gand the other is small mu gand we have some equation for thatbut anyway for one conditionso one side is 0.99and the other side is 0.01or something so such differenceso very large differenceand if you change the conditionthen it goes to greenthen if you change the other conditionit goes to redso it worksso this could be apossible explanationand actually this is a very simple modeland experimentalist didcomplicated model but basically same ideaof courseyou canyou already expect that okay this worksnoise strength should beappropriate rangeif the noise is too smallmaybe this can be still stableand if the noise is too largemaybe this can be kicked away alsoand then it goes hereso actually we cancheck that noise strength leveland howthe fraction that good state is reachedso we do several simulationshow the fraction that good state is reachedand so within some regionso around this 0.1to 0.3 or 0.4this good region is selectedbut if this is 0.01or something then basicallystill half and halfand if this istoo large again it starts to decreaseand then finally maybeswitch to itso this is a possible explanationfor this kind ofspontaneous adaptationand maybe this is generallywe can discuss that okayin an active stateboth the synthesisso in a good state synthesisof course in a good stateso that dilution is fasterand this synthesisis also large so they are balancedand in a bad state both are smallso then put noisethen good stateis selectedso that's a proposal for thisand actually there is no direct confirmationthat this really works in that experimentbut only manysupporting suggestions thereand one difficulty here is thatit's not easy to estimatethe noise strength in this cellso if we know okayin this cellthis noise level is something around thisthen we can expect thatbut so far we are not surethat's one problem herethen maybe I should stop heremaybe I'll talk abouttomorrowmaybe this is generalized to some othersI hope to mention some beautifulexperimental setup of thiswakamoto's group but maybe you canyou can know thattomorrowok questionsok see you in 24 minutes initially I did not expecthad not planned to talk about this