 Vse, zaočne, že sk資om na tem pristavke bovoste z autoritvarzavstv enstavnih, z kako naziv si tudi tudi za 9, in pas te glasbe, ki je 9, in tudiKorean, so ne bo tudi za 9. Ok, res predstavno, na 5 vs 9 bo Evreni ne biti po investiki in za vse. Ok? Zato prejdo so vse več, ne pitajte dl trace eskubiti za 9 vs 5, zelo sem nekaj to nekaj to nečešnje. Daj. Ok, zato. Spodaj. Zvukam, da sem ovo zelo tako zip. Tko je zelo v vsej vsej. Zelo vzelo vzelo vzelo vzelo vzelo vzelo vzelo vzelo vzelo. In ... ... ... odrečim vzelo vzelo vzelo vzelo. And then I go to the next, so today's, yeah, talk. Here just a simple origin of a long, log-normal type distribution. So this distribution of sub-abandones, this shows this kind of a long tail. And log x, this is close to Gaussian. So there is another simple explanation for this, and that is related to some experiment. So basically, so this is an experiment, and you don't need to go into the details, but only this part. Or maybe even this part is not necessary. Only this is used for regulation. So what in this experiment doing is this, this is gene, and this is expressed. So messenger RNA produced, and then from that protein is produced, as you have heard from Central Dongma yesterday. So in this experiment the other part is some kind of regulation to suppress or something like this. So by that, so this expression rate K is somehow experimentally changed, controlled. So basically in this case this is expressed and this is so maybe degradated. So simply this concentration of this protein, x is produced and then just decreased. But furthermore, this cell grows. So this cell, so with this growth so every component is diluted, so this. So this is without any stochasticity. So then if you have some noise in this process, maybe this expression level is changed. So maybe eta t, eta gt, or something. And then, OK. Then maybe you have heard from this Fokka Planck equation in the first two lectures or something. And then you can see that this shows Gaussian distribution. So x shows this if you have some usual large van noise and from the Fokka Planck solution you can see this kind of Gaussian distribution. But actually this is different from this. And one thing that is missing is that mu, this growth rate itself is fluctuating. So if you consider mu eta v, t or something like that, then this here is that you have a term. So this is different from usual linear large van equation. And you have what they call multiplicative noise. And by that, so this shows this kind of long tailed distribution. So maybe you have heard, OK. So you learned, I believe you learned the Fokka Planck equation from Holhez lecture. And then, so according to this large van equation you can get this kind of Fokka Planck equation. And by solving this Fokka Planck equation so we get this kind of, this type of distribution. So maybe this is, I don't think I have time to go into details of this. So maybe as a kind of exercise you can check that, this kind of what distribution it has. OK, so this kind of distribution and then OK, maybe I think of this. Yeah, so actually with this kind of solution so we get this kind of distribution here. And the different color corresponds to change of k. So with this experimental technique by controlling this, some other external parameter you can change k. So by increasing k, then you can have a different distribution. And then, so this is measured, this x. And as I said previously, there is a technique, flow-site meter or flow-site meter or another cell-sorter. Flow-site meter is a technique that cell is. So flowing here and this laser and check fluorescence or cell size. Cell-sorter is a kind of a little bit advanced. By according to this they choose one cell here or another cell here. So they choose, for example, large cell or fluorescent cell so they can select that. So biologists use these kind of techniques. But anyway, so you can measure this distribution and that is what they obtain here. So this kind of distribution. And then, so what they say, GFP versus forward scattering. Forward scattering means in this, they measure by that. So forward scattering, they can measure the volume. So basically fluorescent versus volume is the concentration of the protein. So by that they can measure x of each cell by cells. And they can do this very fast. So in an hour or something they can get maybe 10,000 cells distribution or something like that. And by that, so they obtain this distribution. And then taking log, you can have this kind of distribution. So after taking log, roughly, yes, symmetric, right and left. So it's closer to log normal distribution. So, and actually, so we can check this that, okay, using this kind of Ranjava equation and the solution agrees rather well here. So in this case, so there is a question that this noise and this noise, which is larger and if this noise is much larger, basically you can neglect this, then usual Gaussian distribution. But if this noise is larger, then this kind of multiplicative type thing and then it shows a kind of long term distribution. And so at least in this experiment it's shown that this noise in the growth rate is more dominant than this. So stochastic expression level noise of 2k. So that's a kind of additional comment for yesterday's stuff. So I go to the next topic. So if you have some questions or not, then maybe I go to that. Okay, so I think I already started talking about this cell reproduction process. And so I talk a little bit on this kind of reproduction of cells. So in a cell there are many components here and then cell growth and device and so how this kind of reproduction process is achieved. And actually, such kind of problem has been experimentally so being done or being done to make a kind of artificial cell in laboratory. So they put something into this kind of within this membrane and put these things and try to make a kind of artificially growing and dividing cells. And there are so some advances already. And of course that is related to the question of this origin of life. So that's a long term unsolved question in science. And so how just initially chemical reaction process is going on and from how this just an ensemble of chemical reaction and this cell, reproducing cell, there is difference in how this has happened. So that's a very basic unsolved question in science. And actually there are many so experimental and theoretical discussions for this. So I just mentioned a little bit on this and then some more, a little bit more thermodynamic property of a cell and so minimal cell. And then going to talk a little bit on some kind of consistency of reproduction and molecular replication, how it's broken and then cell may go to sleeping state. And actually that is also universal in many bacteria or another microorganisms go to a sleeping state in a bad condition. So I hope I talk this today. OK. So actually the basic question in so I do not go into details of this original life type program, but maybe just I mentioned and maybe I hope you can learn by yourself, is that OK. Yesterday I think you have heard and then the important point in this biological system now has OK, there is some kind of metabolic process and enzyme and make some energy and then keep the cell state for growth and so that is kind of OK, metabolism and for metabolism to get energy to work, then you need enzyme, catalytic activity. So that is basis for living. But as you know there is another important issue is that genetic information. Currently, current cells so we have DNA and from that so information is transferred to the next offspring. So this genetic information is necessary to produce this enzyme so as you have heard in Central Dogma. But for this genetic information replication process of DNA they need enzyme so it is a kind of mutual process and so then considering the origin of life so which is first that is kind of maybe chicken egg type problem so chicken or egg it is and so so there are many discussions on this so how this process started so this, but currently these two are rather separated so these are protein and these are DNA. So one possibility is that originally original cell system or original cell or proto-life system may have something both a little bit and then both so initially they have both and somehow they separate so that is kind of hypothesis of RNA world and so some primitive RNA have both nature and then so one guy is one type of molecule so specialized for this and one another type of molecule so that is one hypothesis just to clarify the hypothesis of RNA world is that both the sort of metabolic part or the energy so RNA world hypothesis I'm not I'm not a strong supporter for that and so at least they have found that some in the catalytic activity so some RNA can have so this genetic information and also a little bit catalytic activity some RNA have that so that discovery accelerates the view of this RNA world but how this occurs nobody knows so maybe this may occur as a symmetry breaking and actually I don't have time to discuss this but a few years ago Takeuchi and myself proposed that maybe some kind of symmetry breaking process leads to this kind of separation so but that's also kind of hypothesis theoretical world it works but I don't know if it really happened and another possibility is that this is initially this world exists initially this world exists but then they don't have genetic information so this kind of reliable faithful replication cannot happen but at least some kind of metabolic process is working on a functional exist and later genetic takeover so I think one issue is all of this should happen in a confined environment I hope to write so membranes are mostly composed of lipids I was speaking of writing in the next one actually these three are essential so somehow they membrane and enzyme is encapsulated and then some kind of genetic information so ok this and this how these so join it's also a kind of question and genetic takeover theory is that so essentially in this RNA world there should be also a story of how you do you do the membrane with RNAs so far no no so there are some arguments that initially there is maybe membrane does not exist and then you have some kind of small porous media so in some kind of in a rock there are small porous and then these works as a kind of small porous hole can work as a kind of external membrane and then somehow they find some kind of so external kind of hole porous media and then somehow membrane is invented or takeover or something like that but that's all kind of hypothesis yeah hydrothermal so in this hydrothermal in this or sea, bottom of sea there is some kind of volcano and around that hydrothermal and then there may be some reaction going on and somewhere here and then they may have this kind of process so that may be plausible but so far there is no proof and as for the relationship between this and this so for instance maybe you are all most of the physics students so you know, Freeman Tyson so this Rina of Physics and he has a theory that initially this and then probably somewhere this kind of genetic takeover occurred and I recommend his book of this it's a very yeah just 100 page small book but it's a very good book and I recommend you can read this in just a few hours but anyway it's a very good book so he proposed he insisted that initially this kind of world exists and he has some kind of icing model type simple model so very spin model active or inactive molecule so this is represented by easing spin icing spin and then he discuss probably somewhere this occurred but there is no theory for this so there are lots of yeah mysteries here ok so I cannot solve this yet so if you are interested you can try to think about this ok so this yeah actually initially this is this Freeman Dyson picture and maybe this kind of replication this kind of genetic information by RNA first is that maybe one famous person for this is Manfred Eigen and so Manfred Eigen so who is a Nobel Prize winner chemist and he discusses this possibility and but he pointed out several problems for this and what is called error catastrophe that sometimes it's due to this error this information is not so well sustained so there is a serious problem here and he discusses this problem and he try to answer so how to solve this and he propose that several so what he call hyper cycle so some reaction molecule supports the other in some the other mutually supporting molecule so catalytic molecule reaction set can solve the question but then he also found the problem there so and from that he finally showed that this is necessary so these are somehow linked with each other so yeah so that's an interesting question and also there is ok so basically if you want to make this kind of problem in the experiment then if you want to do that probably one needs to put some kind of ok you want to make a kind of minimal protocel that maybe you need to make a membrane and put some kind of enzyme and then some kind of genetic information material maybe DNA or DNA and from that this enzyme is created and then probably from this enzyme or some other protein maybe membrane is created and then also this enzyme should be produced and by that this is replicated so if you make such kind of experimental system then maybe you can say that or something like that and people are trying to do that and actually my colleague started this kind of 25 years ago or 30 years ago and so I supported this group and so they are kind of little bit progress and so ok so for that maybe some nutrient is necessary so but this is externally supplies so that's a kind of minimal cell construction and people are trying to make this kind of minimal enzymatic reaction metabolism and actually some Japanese produced a kind of simple no not simple it's some kind of model of this no not an experimental system of this with 144 species of vivo molecules and they put this into in vitro these reactions of these 144 chemical species and this RNA and some other molecules and then they succeeded in that this can continue to this process and some producing jet information but not membrane itself so still this is not simple at all and actually they are not producing from this scratch they all these molecules are extracted from the bacteria and they minimize this try to minimize this reaction and found this kind of system what they call pure system but this still for physicists is too complex so actually but they know all the chemical ingredients here so actually Matsura and others made a kind of simulation of these 104 species and these 5000 reactions and they can produce that this can going on but still in the experiment usually this cannot sustain so long and some kind of a waste chemical and so finally after some hours this process stops so still it's far from and as for this genetic information plus membrane so even though they cannot make a membrane by themselves so they put this kind of so oil emulsion and RNA and enzyme so they make this kind of system and try to evolve this system so this has been successful and you can see some paper by Yomo detail this so if you are interested in maybe you can check some of these so but I do not go into details these are very experimental but this is also theoretically interesting because there is a problem of parasites or some others and how this evolution occurs so they found this interesting process so maybe you can check this okay so there are so many experiments but it's okay so now okay we come back to theoretical discussion so we try to understand kind of minimal situation of this and so at least you need some kind of so for the moment we do not discuss so much about this so then what we need is that nutrient from enzyme created and this enzyme is created and membrane is created so for the moment I forget about this information so now this process is usually believed to be non-equilibrium and if you have read Shreddinger's book of this origin of life and then at the latter part he showed that non-equilibrium condition is necessary for life so how many of you have read Shreddinger's book of what is life okay that's a very old book so this famous Shreddinger so in the first part of the book he kind of predicted what is genetic information what type of molecule carries on the genetic information and then after his prediction maybe ten years of something like that so Watson, Crick and Rosalind from Shreddinger showed that in this DNA structure and in the latter part he discussed that non-equilibrium condition is important to how life does not increase entropy so he proposed that life system is negative entropy so that's the latter part of his book so somehow non-equilibrium condition here I pointed out the importance of enzyme and actually enzyme is encapsulated within so outside enzyme does not exist so enzyme is within this membrane so that structure is quite important so here I won't discuss encapsulated enzyme so importance of compartment and catalysis and so in this system so maybe by this membrane produced and grow and maybe later may divide so this is outside is so how non-equilibrium it is tricky point because when you discuss for example carno cycle or car engine you need two baths and by that give some energy to this and they can make some kind of heat engine but here usually outside is outside is not necessarily non-equilibrium just you have some kind of nutrient here and some chemical chemical molecule here so basically of course this flow occurs so that part is somehow probably non-equilibrium and then this grows and divide so basically this system so I point out this enzyme is quite important the reason for this so maybe by this so enzyme is catalyst molecule so you learn that catalytic molecule catalysis does not change equilibrium condition only change the speed chemistry or thermodynamics so consider that some kind of process that resource and catalyst some make product plus catalyst and then this reaction is bi-directional and they say that equilibrium condition between resource and product so equilibrium condition by resource and production production for resource so this equilibrium condition does not change by the existence of catalyst still in a biological catalytic molecule or enzyme this speed change by the existence of the catalyst is enormous so maybe 10 to the 10 times faster so that means if you have enzyme here catalyst this reaction can occur resource and product catalyst does not exist this reaction basically does not occur in our time scale maybe if you wait forever maybe finally it goes to equilibrium to go to this state but otherwise without this existence basically this reaction does not exist if the reaction does not exist in the outside that means you can have this ratio can be anything because R and P are kind of totally disjoint so cannot change by the reaction so it can be arbitrary but within the cell you have catalyst and once this comes in for example product resource is coming in then this reaction occurs and then probably this catalyst works so well then it's equilibrated so this is a little bit strange situation external world is no equilibrium anyway so it can take anywhere but once it comes in within this membrane there it goes to equilibrium so in some sense cell is a kind of a system to make the system to go to equilibrium so that's a little bit counterintuitively or different from usually discussed but as far as I know this catalyst works so well so that means this time scale is so different so this could happen so I think this is important so basically in that sense cell is a kind of equilibration apparatus to unvej external no equilibrium condition so maybe this product does not exist at all or something like that then once it goes here it's going to equilibrate but of course it's not completely equilibrated because they need enzyme and growth and they need membrane or something so not perfect equilibration but so this point is quite important and actually probably one of the important point of their life system or invention of life system is this catalyst so they can change the time scale of their reaction enormously so by that they have their own time scale so that is I also come back to this point later for a different biological topic but with this change you can change the time scale so that's basic argument so by that I just talk about this kind of thermodynamic efficiency of this system so I take a very simple model so this is what I said most reactions are facilitated by catalysts so it is sometimes like that and so now, ok, here I sometimes resource and I sometimes write nutrients so this is now nutrient so the simplest model for this is that nutrient and then this enzyme is produced from this nutrient but this production is used by enzyme so this is kind of the nature of what they call auto catalytic so they catalyze the process of this to produce itself and also they make some kind of membrane type molecule so kind of what I call here membrane precursor so this enzyme and nutrient or maybe nutrient one produces enzyme so nutrient one so you have nutrient one that produces enzyme and nutrient two this enzyme produces membrane precursor and membrane precursor is attached to this so this membrane molecule is attached to here and then grow so very very so in some sense much simpler model than the one I talked to yesterday so just see membrane molecule, membrane precursor molecule and the enzyme and nutrient the fact that nutrient comes in and does not go out it's also non-equilibrium otherwise you would have zero flux that is necessary so it's coming in the membrane so somehow makes this kind of capsulated enzyme so if enzyme goes out freely and then this concentration outside inside is same then it does not work and it's essentially because you have the enzyme that consumes the nutrient that the concentration inside is less than the one outside so so this is so simple model so so so sometimes use nutrient and I sometimes use resource so N and R are basically same so consider this model and then discuss this model then basically you have nutrient or resource chemical enzyme and membrane and here we assume that X as the enzyme concentration here and membrane precursor concentration is Y here and then you have resource so with this reaction process of going in here so you can have enzyme is produced from resource so this kind of resource and enzyme and catalyzed by this that means change of X is proportional some coefficient and catalyzed by this so it's proportional to X and then this reaction going on ok with this K and we take this one so it comes back so this is kind of this reaction process so this reaction is catalyzed by this enzyme and going forward and backward and maybe forward rate is K and backward rate is 1 and then Y membrane precursor is catalyzed by enzyme so it's again proportional to X and then ok maybe you need some other proportional coefficient and then again so basically you have resource so in this case so nutrient membrane and with this L to 1 and catalyzed by enzyme so that's and again this ok from this first membrane precursor is put to this membrane so with some rate so maybe and that is attached here membrane precursor, some molecule exists but it's attached here so this goes like this ok that's this model but also with this growth so membrane is produced and then cell volume grows so again with this growth so take this so it's diluted so this is a simple equation and you can make it state easily so nothing very special interesting solution exists for here so we can set up this ok, yes so we are talking about life so no, just so here lambda growth rate is a parameter, right? so it's a hydrogenous determined by the properties of reactions so you could say lambda equal to zero or even lambda negative, right? ok, but lambda, ok, where is that? ok, lambda should be ok, lambda the ratio that membranes produced and by this production so addition of membrane volume increases so basically lambda is proportional to this membrane production so this is membrane production so basically this then maybe with the structure maybe there is some other proportion coefficient and this we assume is a constant why? so this is the ratio that membrane is produced from that membrane molecule decreased by this and accordingly it's produced but maybe so there is some kind of transformation ratio so that corresponds maybe to this yeah so this is kind of very if I understand correctly the point is that this is a equation for the concentration you could write equivalent equations for the total number of molecules and then it will become you will not have that term minus lambda x and minus lambda y but you could immediately interpret the growth rate as the change of the membrane so basically so maybe I do not discuss about the structure of membrane so much or if it's fair but basically simply I assume that this membrane increases and then the volume increases accordingly and this proportion ratio so so this is kind of set of equation and then we can, so this is a simple equation so we can have an easily go to steady state solution and then we can discuss the nature of this and then of course with this nutrient so cell can grow because enzyme is created and with some ratio and then what we want to discuss here is that kind of thermodynamic efficiency so maybe in the I guess in the first lectures maybe you have known that some kind of importance of entropy production entropy production that is loss, so thermodynamic loss and this is basically done by this kind of flow versus if there is some kind of reaction so there is some kind of chemical flow for each reaction and chemical affinity then so actually this chemical affinity is that basically the equilibrium condition to forward and backward ratio from that you can compute and then it's going to this entropy production is something like this ok, this affinity and this is flow rate and this is another reaction so for this reaction and can I ask another question, sorry you also need to have an equation for R because R is not the concentration outside R is given I assume that this is supplied constantly so it's a kind of constant external external parameter so nutrient maybe if there is constant supply external concentration and according to external concentration it comes in so then ok, we check this kind of entropy production so this is entropy production and then for power growth how much entropy is produced so we can discuss this entropy production per volume increase as sigma over lambda so this is entropy production per volume increase so the point here is that if this is small maybe the loss is small and so we learn from Carnot cycle that when we put the system nearly near to equivalence make very slowly to change then the efficiency is highest the loss is minimal and so the question is that if this is true or not so here so ok R is basically externally supplied so if this external resource supply is quite low and slowly it's coming in so it's somewhat kind of a very slow process so what maybe we learn from quasi static condition or something like that and then the question is that what is the function of external flow of resource so usually maybe Carnot cycle type thing suggests that ok equilibrium in the case of equilibrium Carnot cycle is something like that so external resource flow is nearly zero this is almost this so if you try to make this faster then the loss is larger and in this system from this calculation of this steady state and this value we get this behavior so in some sense for this cell if it's very slowly increasing and just taking resources slowly and very slowly it's not so efficient for this cell it's better to move in a kind of fast speed but if you increase much faster maybe the loss increases and the reason for this is the nature of this enzyme so if you have more resources you have enzymes produced and if you have enough enzyme the system approaches equilibrium so if the system is near to approach the loss is smaller so in that sense if nutrient resources is small the enzyme is not sufficiently created so it's still far from equilibrium but by making enzyme more so that's why this kind of thing occurs the losses decreases but actually it cannot go to zero because this cell can produce other membrane processes and this part has also entropy production so the loss by producing membrane growth so this increases by membrane growth and so volume growth so by that this increases occur but this is approach to equilibrium by enzyme so this is somewhat interesting so there is some kind of basic loss if you have this cell this cell is put in a kind of minimal condition so that's one interesting aspect of this cell when you consider this OK, so how much can one apply this understanding to real cells in the sense that we discuss in proto cell or say origin of life that essentially in real cells you have mitochondria you have energy say ATP molecules and things like this which are driving essentially systems out of equilibrium inside the cell so I do not know exactly that I'm sorry for this but it looks like if this cell somehow more efficient if the cell is not so usually when the cell does not grow it's not so they lose a lot of entropy increase the entropy and production so maintenance energy so they need some kind of maintenance and then this may decrease first by growing that so staying just there is not so efficient for this cell and that seems to be OK but exactly for this I'm not sure so OK so this is kind of a simple example of this kind of a simple cell argument of this law and then OK, there are many other important laws in a cell and but actually so the other speakers are talking about this Mono's law and this Shekht Scott who are law so I'll skip that so this is a kind of general law how the growth rate depends on this external resources and of course it's interesting how this kind of simple argument is related to more biologically established law so this is a kind of question to be resolved but for these kind of laws please maybe they will talk today or tomorrow I think the other lecture so I skip this kind of famous Mono's law growth rate and other RNA amount versus growth rate or some such kind of law so they will talk I believe OK, I just maybe 20 minutes I think I mentioned a little bit about so the transition to sleeping state and one general issue in this kind of primitive cell is that always there is some kind of waste chemicals so here so I produce these kinds always enzyme and always membrane so no other components are produced with this reaction so that is in some sense the action but actually in the reaction process in a cell producing enzyme these itself is a kind of long polymers proteins are long polymers so you have long polymers and then so protein is so in a certain sequence of amino acids they are kind of good protein so with this some sequence maybe for physicists it's better to use I think model type representation so maybe this kind of sequence this is good good means that catalytic activity so but this reaction process produce this polymer sometimes there is error and that is unavoidable due to thermodynamics so there is some temperature so it's not completely so always completely same molecules are produced sometimes this goes to this or something like that so some sequence and then so usually this catalytic activity is lost and that is kind of waste chemical and actually this kind of waste type chemical is not good by itself but it's also it can attach to good molecule or something like that and then suppress this process so in this usually in this experiment of cell there are some molecules, some protein molecules aggregate and then attach to some other and aggregate and then so this can suppress this and that's always unavoidable and of course in the present cell there are some techniques so cells invented to have some kind of other enzyme to kind of make a kind of disposal and so to eliminate this sorry but even in absence of disposal just because you grow you dilute the growth is important so if it's growth of course waste chemical concentration is diluted but if it does not grow in some sense it's difficult this may be aggregated and that may happen so you already Winston Churchill says that growth growth so there is some growth ok, growth hides every problem so so yeah so actually if you have waste and maybe if the city just grows then this wasted proportion is decreased so of course growth is important growth can solve this waste accumulation so but that means if the growth does not work this may be a serious problem and actually in the experiment of prot cell usually they sometimes go to this problem because sometimes growth can not work so well and then this waste chemical is more accumulated aggregated and that further suppresses growth and it goes to that state and finally it collapses so that often happens in prot cell experiment and probably that still exists may exist in the present cell even though there are chemicals or something it may still happen so that's the discussion of this sleeping state ok, usually when you have cell and they put this cell so bacteria, so this is a kind of present bacteria experiment so bacteria into some nutrient condition and then the number of cell so after some lag time they start to increase and here they basically increase exponentially so this is log scale and then at some stage they stop the growth and they no longer grow basically this is because nutrient power cells is not enough and they stop and then they are going to not grow not die so they are staying some kind of sleeping state so cell are there still not dying and then after long time they may start to die so there is some different phase exponential growth phase and sleeping state, dormant state or such kind of name uses dormant state so basically sleeping state so there is a transition from here to here and that is quite general and that is theoretically interesting because usually in the yesterday's talk usually this kind of auto catalytic growth so x produces x so some kind of process is going on in that cell so that means the abundance of chemicals growth so basically the processes so the number of molecules there and this is positive then it grows exponentially so that is exponential phase so this number increases exponentially that is easy to understand then the sleeping state means a equals 0 while if a is negative in a bad condition cell cannot grow and finally it disappears so this is death so you have some condition external condition or something usually we can think that this growth rate is maybe in a bad condition tie that is easy to understand so here this growth, here die sorry, just to understand is a equal to 0 state so is it that cell do not reproduce or that they reproduce but the reproduction rate is compensated by the death rate in this case so there are some cases but at least in some cases cell, each cell does not grow so some grow and some dies and it's not balanced that is not necessary at least in the dormant state what they call dormant so they just do not grow so every cell is something like in some condition a is nearly 0 so usual simple model shows this, this goes here and this negative to positive and this position is just single in a usual simple model and then how this is possible so that's a question and so the proposal here is that this may be related to the problem of waste so here maybe waste chemicals is accumulated and then suppresses the growth and somehow this waste chemical and this production is somehow compensated within a cell and so that this state exists so that's a simple idea here sorry, just to be sure so the idea is that in some sense waste is a regulator of growth yeah, waste suppresses and aggregate molecule ok, we did this model about some time ago yeah, this one ok, so so now we use resources s, sorry sometimes n, sometimes r and this is s ok yeah depending on the collaborator we use a different notation yeah, basically it's an external substrate resource and then it goes to some kind of important enzyme and actually enzyme, ok, here, active protein auto catalytic active protein so we call A but there appears some kind of waste or inhibitor so this is waste, B biologists like to say that ok, this may be inhibitor of growth but I like to use just waste so basically s and resource and A and B and so another issue here is that this waste chemical attached to this active molecule so they make some kind of complex molecule so another process here we put is A and B make some kind of complex but A is active protein so that works as enzyme and catalysis but when it's attached to by B it cannot work so maybe you can think of this protein, how protein makes catalytic activity so they have some structure protein and then A protein so some structure makes this structure makes some kind of catalyst so in many protein science book you can show that this kind of some structure works as a kind of function for catalyst but if B is attached here then it cannot work ok, so this is a very simple kind of toy model so resource and A and B and it's produced from here with some ratio and then A and B make some kind of complex so basically the reaction process is that and S goes to B catalysed by this and A plus B makes so then you can write this equation ok, basically so resource, ok, maybe A is produced here and with the ratio of this function of A and this is ratio of function so then you can write down this increase of S, A is that produced here and by that, ok A plus B produces C so that means dot, with this A decreases B plus C with some if this is forward, this is get something like that so this is GAB ok, so this is the process to make a kind of complex and by making a complex, A decreases with this complex production AB and then the ratio of A decreases and then, ok, if you consider this so forward and backward reaction then it's increased from C so this is AB minus C basically so this function ok, maybe then this protein maybe decomposed with some rate but these are not so important maybe you cannot forget about this and again this growth cell growth, it's diluted so again previously I used lambda but here the growth rate is mu so mu is mu is ok so and then, ok C is this ok, and resources external resources given from outside ok, it's changed to transported to internal state by A and then resources used to A or B, so this is decreased and this is also diluted by the volume so you can think of this model and I'm not sure ok, one another addition in this model is that ok so basically from resource A or B is produced so here we assumed that F-A is so in a good resource condition so always good molecules produced but in a bad condition so maybe more of this waste is produced so there are some reasons to assume this, usually to produce good molecules they need some energy so in the process of reproduction, replication of molecules usually as I said there can be many errors but in the present cell they have some kind of mechanism to correct the erroneous molecule that is called kinetic proof reading so basically there is some kind of error correction so if you make some kind of molecule sequence often there are some kind of so mis, so sites and then this can be corrected but this needs some kind of energy or this resources by that so we can assume that in a good condition, ok always more correct molecule is produced and in a bad condition so this fraction is larger actually this can be you may find this is kind of ad hoc in this model but we can think of other models that does not have this but still we can get this kind of result ok so maybe I think I finish in a few minutes so I show the results ok basically the result of this kind of so according to this result you can compute how this kind of so resources coming in and according resources coming in then this volume grows and so you can compute this growth rate mu as a function of s according to this model and then the result is something like this external nutrient condition is decreased but at some stage it goes down so mu is this it goes down drastically so maybe it's not exactly zero but it's very close to zero so and then ok if you do not consider any decomposition basically this state remains but if you have decomposition maybe at some point maybe it goes to death state so basically you have kind of active and sleeping state and death state ok so I think maybe ok here so basically this transition occurs here basically active molecule exist A is dominant and very little B and very little C but here so you have more B and this fraction of A decreases but it's still not zero it exists in this reaction process it remains here so A active molecules is trapped by this so this is the state so active molecule is trapped by this B so this is a sleeping state and that is important because in this kind of auto catalytic system if A goes to zero there is no way to recover because A is necessary so if A goes to zero the growth is not recovered so usually in that model so as I said previously this kind of thing occurs so maybe in this case and then in a bad condition if A goes to negative and A goes to zero but in this case so A is hidden into C A is into this C C is A plus B so even though it still slowly exists here and then when you regain the nutrient this comes out from C and then it can start to grow and actually this is such behavior is generally observed in a bacteria so bacteria they put into this bad condition they no longer grow and stay there and then if you regain the nutrient after sometime they recover the growth like this B or bad conditions like antibiotics for example B is increased by antibiotics or maybe so the typical experiment is that just cut the nutrient and so they starve and they starve and sleep and so that's how this kind of behavior appears and then ok maybe I should stop here ok so maybe I talk a little bit more other questions not from Matteo ok so I think we can go to the break and be back at 11