 Kaj je inštačno, da smo počkali? Zdaj, kaj je inštačno počkali? Dobro, sem glasba, kaj je. Zdaj sem vseh P.H.D. studentov na EFOM, v Milanu. Zdaj je izvršenja, ki je vzivno skončil na kanserice. Vzivno, ki se dobro vseh, da imamo model, ki možemo ještječne zvršenje dajselebe. V mene, kaj sem izvršenja, da je vzivno skončil na grojt. Zdaj, zelo vseh, da vzivem, da vzivem, da vedem, da je vziv, da je vziv vziv, da se vzivem, ki je vziv. When a cell is exponentially growing, the state of the proton composition is tightly related to the growth rate. For the proton we refer to the whole group of proteins that are expressed by a cell in a certain condition. In triple smo je pravdi, in je to upbeeping in je je, da je naspežen, in je to pravdučezne. In je tje, da je, je dološen klasifikacije, da vam je zelo vse dolačen. kapožena je otvarjana do zelo, učil je ještje obježenje obježena. Tako chill do zelo, da je stranje z delovмет, da je na sel milit producez čest, se pričo se priče, je tko, da pletuje cel zelo, da je tkaj preč postel, ker bude zelo, da je počet, in zelo, da je ta otroj sektor ubil, That's what we usually call phosphor. The relation arises because of the problem in research. Cell needs to be clears, so a time that synthesizes the cell so we can build up mass. But in order to do that, cell needs aminoacid and other precursor in prišli in godzimi zelo, tako gre, da reprežite zelo vse, ne zelo se, da ležite, batteri nismo, tudi nekih, tako, da lahli, ki so ta nisi na večelo, ki se rečijo, k Clo, ki je nekaj vse, nič si je, da so nekaj, praying vse, da jo se ko opreživajo, Kaj je izgleda iz teori, kaj je izgleda izgleda iz regulatoriji, kaj je izgleda iz regulatoriji strategij. V Bakteriju je zelo, že PPGPP je izgleda, kaj je izgleda izgleda iz izgleda iz izgleda iz izgleda izgleda, in odpičen je državnjo, ker PPGPP je odmah, če je izgleda, kaj je izgleda izgleda izgovoril je zelo. Paj zelo izgleda zelo, da izgleda izgleda izgleda, zelo izgleda se z vrča posložnoj, kaj je izgleda izgleda izgleda izgleda izgleda. In razliš page n integration of these two issues. So I'm going to introduce now our framework, which is composed of four main parts. So the first ingredient are the regulatory functions of the pros and sectors, which is basically the function that tells how the... s nekaj človpoundovčke, tudi nekaj človrbi človrbi, s veči človrbi, in sljup in v koristice, kar je, da je, da je, kot jo, izgledaj, to, da je, da je, ko, da je, in, in, neko, dahe, pomagaj medicines nekaj čel in zelo pa, da je svoje rezačne, skupno nekaj trvalovač nekaj se možete kratilo dopelju končnosti, več, da je minimija protem, zelo je sektor, kaj nekaj je propr Performance mass, in tudi je nekaj idej za akumulacij Tačnojga. Na predrha, In z nekaj načajo ga se značila, da je skonjunga prijeljna biomaska, je tudi skonjunga biosynthesima vriste, k če nekaj je vrtele neko je skonjunga vrste spesivnje sektoris, je toz bilj nači vrtele vrtele tudi s Kaj. Se to je kanal u vrtele vrste. Tako je tudi sektor misljenja dešne spesificije. in zelo se počutno počutiti, kako se izvajalo, da počutno počutim začet večen, je veliki na večenom zelo. Na večenom, kako se načale, nekaj da se začet na večen, je veliko na večen. OK. The next ingredient is to understand how the value of the regulatory function arises. Because we want to know how the ribosome can know how many ribosome they have to produce, how many housekeeping protein and constitutive protein. The fact is that the ribosome do not know those particular ratio that they have to produce the protein. They just randomly attach to the mRNA and start transcribing for whatever is code in them. Therefore, we think that we propose that the regulatory function, their value, arise strictly tied to the composition of the mRNA pool. And we define the regulatory function as the fraction for the sector i as the fraction of the transcript for that gene i divided by the total transcript. So in order to understand the dynamics of the regulatory function, we need to look into the transcript dynamics, which is given by a production term beta p, where p is the RNA polymerases, and the degradation term. This for the total transcript, while if we look at the transcript for a particular sector, in this case, it's written for the ribosomal one, we have that the production term is multiplied by a function omega, which is really similar to the regulatory function for the proton synthesis. Here, omega is telling us how many RNA polymerases are transcribing for ribosomal gene, in this case. So putting together the two equation for the transcript dynamic and the definition of kylet was in the other slide, we found this equation for the dynamic of the regulatory function. And also from here, we can see from this equation, and the one before, we see that a steady state requirement is that omega equal ky equal pi for any given sector. So in bacteria, we know that the PPGPP is the one that sets how many ribosomal transcript I'm going to produce, because it interferes with the binding of the RNA-P on the ribosomal promoter. Therefore, omega R will be a function of the PPGPP level, and we set this function by the fitting of steady state data. OK, the next ingredient is to understand how the level of PPGPP is fixed. And in this case, we choose to adhere to the last paper by Teriwa's lab, where they basically found an empirical relation between the PPGPP level and the elongation rate, the transition elongation rate. In general, the PPGPP level will be determined by a term that represents the synthesis of the PPGPP and a term that represents the degradation. And the co-authors in their paper, they propose that the synthesis term is proportional to the dwelling time, which is the time that the ribosom, after the elongation is the time that the ribosom waits to get another charge tRNA, while the degradation, and this time is, of course, also related to the abundance of tRNA, of amino acid, and other elongation factor. While the degradation of PPGPP, they propose that it is instead proportional to the time of translocation, so to the time that it takes for amino acid to get incorporated into the protein and for the ribosom to move to the next code. Put in together this equation with the definition of the translation rate, where the inverse of the translation rate is given by the sum of these two times, we get to the empirical relation between the PPGPP level and the elongation rate. Epsilon tilde is the maximum elongation rate. So basically, when the elongation rate is maximum, we get that the PPGPP level is zero, while when my ribosom is lower, I build up the PPGPP. OK. So the last ingredient that we need is to understand what is the dynamic for the amino acid. And here is relatively simple, because the dynamic is just given by the influx of amino acid mediated by the constitutive sector, where nu is the nutrient quality of the external nutrients, and the outflux, which is given by the biomass flux, because the ribosom that are using the amino acid in order to build the protein, while the minus lambda psi is a dilution term given by the growth of the cell. OK. So I finished presenting my model. I do a quick recap here. So basically, we have that the size of the sector is decided by the regulatory function. The regulatory function are tied to the composition of the mRNA pool, which is given by the PPGPP mediated ribosomal transcript dynamics. The PPGPP level is determined by the speed of the ribosomal elongating. And at the end of the amino acid level is just set by the equilibrium of the different fluxes. So now I will show you the theoretical result that we get with this model. So firstly, we wanted to make sure that our model predicted for a stable fixed point, because otherwise any kind of perturbation would just draw the system of this trail. And we found that the fixed point of the model are stable, and they also reproduce the first growth law, which this is an important prediction, because as you have seen before, we did not use the first growth law as a definition for our model. So this is indeed a genuine prediction of the model. And another thing we can predict is the growth law for the size of the amino acid pool. And we can do that, because in our model we explicitly describe this quantity. And the prediction is that also for the size of the amino acid pool, we get a linear relation, which is increasing in the growth rate. OK, then we wanted to understand the nature of the relaxation toward the new steady state after a perturbation in the nutrients. And what we find is that the relaxation is characterized by damp oscillation. And in particular, you can see that in particular, we have seen that all the important quantities in the model are showing this dynamic, even the size of the sector, which are the quantities that change with the slower time scale. Because in order to change them, you need in the cell need to make new biomass and to dilute the inner composition. OK, then we wanted to study why this particular behavior arise. And what we found is that this behavior can arise under a very wide set of conditions. And it's not mandatory that the regulatory circuit the equation that we show before. The really important things is that between the ribosome and the amino acid pool, it's important that there is this inquiry feedback between them. So we have the ribosome presence, hini bit, the presence of amino acid, because the ribosome use the amino acid in order to make protein. So the more ribosome I have, the less amino acid I will have. And for the other interaction, we have the presence of amino acid in answer the presence of ribosome. Because if the cells sense that they have more amino acid than required, it means that the considerably sector is a bit too big for that external environmental condition. Therefore, it will enhance the production of protein in order to go back to the desired proteome composition. And yes, as long as this feedback between these two quantities is maintained, we get the stable fixed point and the oscillatory. Yes. Yes. String them together. But what is the mechanism to get at the bottom? OK. Basically, we have that when the amino acid build up, the elongation speed of the ribosome. I mean, the ribosome will start to go faster, because they have more substrate to use to make the protein. If the elongation goes up, the PPG. That depends on tRNA pools, not directly on amino acids. Yes, it also depends on the tRNA pools. In our model, that's right. But the first signal that the environment is changing is not on the tRNA pools, that tRNAs are still something that you need to synthesize. So it cannot be the first signal of the environment changing. But the first thing that the cell sends is that there are more carbon precursor and amino acid around. And this will speed up the elongation rate, even if at the very start of the shift, the tRNA pool has not changed yet. So why are they speeding up? How do the ribosomes know they have to go faster? Because the tRNA pool, in general, is not changing. But when I have more amino acid, the percent of charge tRNA is going up, because I have more amino acid around. I mean, I don't just need that. So the amino acid concentration increase leads to a shift of the tRNA pools towards more charged tRNAs and more charged tRNA speed up elongation. Exactly. And OK, next, we wanted to make sure that this was really the reason we see oscillation. And that the present oscillation do not hinge on some microscopic parameter that is not under control. So what we do is to compare two different systems, one with the transcriptional delays, which is the one that I showed you before. So where the dynamic of the regulatory function is given by the dynamic of the tRNAs. Sorry, of the mRNAs. We can see here in the first plot that we get the oscillation. And during the shift, the value of the regulatory function does not follow the steady state relation with the value of the elongation rate. Where the steady state relation is the dash line. But during the shift, it doesn't follow it. And what we found is that even if we force the regulatory function to adjust immediately with the change in the elongation rate, so it adjusts immediately and it follows the steady state relation, we still get the oscillatory relaxation. Even if, of course, the amount of oscillation is different. The growth rate is shown here on the y-axis. So the double time, I think, will be maybe 20 minutes for the post shift and see it better here. Yes, yes, because three hours is yes. OK. Yeah, all the results that I showed you are also supported by analytical calculation, where we treated our framework as a dynamical system. So we studied in values, the stable fixed point, et cetera, et cetera. OK, now, as a conclusion, I wanted to show some experimental evidence of the oscillation, which we do not collect, but we have a search in the literature if someone has seen this behavior. And in the first plot that I show you, here are two different work. And in the first one, we can see some really rapid oscillation of the regulatory function of the ribosome after an upshift. While in the second plot, we can see the adjusting dynamic of the growth rate for bulk shift in between different carbon sources. And in the second plot, the oscillation are not so clear, like in the first one, but we think that we cannot exclude the fact that maybe they are there. And lastly, I wanted to show those experiment, which our partner lab in Cambridge have performed this experiment, where they shift from anemic fluidic device from a medium with glucose to a medium with glucose plus amino acid. And you can see that both the growth rate and the ribosomal sector, as they would have an overshoot before relaxing to the finite state. And in this case, our model can reproduce this trend if we adjust a little the parameter that connect the amino acid pool to the speed of the elongation rate. Unfortunately, in our lab, we cannot do experiment. And this phenomenon is not really well studied. I mean, not that I know. So here, we are doing what we can. We did it that we have. So this is growth rate as a function of time. Yes. It's four hours. But sort of in the mother machine glucose, it's 80-minute doubling or something. And you go to half of that 40 minutes or something like this. So I want to, this is like a population average growth rate that you're looking at? Yes. I mean, the data for the mother machine is a single cell. But what I'm showing here is the population average. But you expect the oscillations to be only at the single cell level and not necessarily be in phase with each other. No? Yeah, that's true. But nevertheless, we see them also at the population level. People, please. Oh, no. I mean, you give a clear impulse at this specific time for all the cells at the same time, right? So if there are some intensive time scale then. That's true. That's true. But I think that, OK, you are giving a specific input. But at the single cell level, there are multiple factors that are important. For example, the phase of the cell cycle where the cell is at that specific moment. So I mean, that's true that the signal should coordinate them. But there are also other mechanisms that can play a role. OK, so to conclude, basically we have a framework that put together the growth load theory with a more mechanistic description of the PPGPP sensing regulation. And the main theoretical result that we have is that we expect an oscillatory dynamic for the relaxation toward the new steady state. As a consequence of this, I mean, this result means that basically if you put in the model the whole chain between, from the take of the amino acid to the protein synthesis, oscillation is what you would expect. And if this is not seen in the experiment, there is probably meaning that the cell is putting some other mechanism in order to avoid, to have this behavior. So last day, I want to thank my group for the support they gave me and all of you for their attention. Thank you. I just a comment. So an overshoot in the response could have a functional role in speeding up the response time for protein changes. Yes, yes. So I was wondering if you compare situations with the overshoot and others without the overshoot. And look at the response time of the new proteins being produced if you can see this. This could be a reason for this overshoot to exist. Yeah, we did not compare that. But yeah, we know that, I mean, there are some paper by Alon's lab. And also other paper that says that the oscillatory relaxation is probably the one that optimizes the timing of the response. But no, we didn't compare the two versions of the model. Also because really, if you put together the amino acid consumption and the ribosomal production, you will get oscillation. So we can compare different model, but my version of the model has oscillation. We cannot get rid of them. Sorry, can you just show that last plot again from the one you fit against? This one. It seems like the ribosomal mass fraction does a less of an overshoot. Is that something you expect? Or is it just, if you normalize it, is it sort of self-similar eventually? Even in your model, it seems like there's. I mean, I think that also in the model, this example here, the ribosomal fraction is not oscillating as fast as the other. And I will say also the amplitude is a bit different. Because as I say before, in order to change the protein composition, you need to produce new mass. And to dilute the inherent composition that you had before. So for sure, the time scale and also the amplitude of the oscillation of the sectors is reduced, respect to, for example, the one of the elongation rate. I don't know if I answered. Sorry, does your model give any indication of that lag time, like a mechanistic understanding of that phase shift between ribosomal fraction and growth rate, or could it? I mean, we did not study that specifically. But just by looking at the equation of the model, I mean, the way we modelize the shift is that the nutrient quality, nu, basically goes with a jump. And what happens is that the derivative of the amino acid is discontinuous. And so is the one of the elongation rate. But then, in order to arrive from this to the production of new biomass, you have first to change, to adjust the mRNA pool with the time scale tau, which is 10 minutes, around 10 minutes. And then, you have to adjust the size of the sector, where the time scale here is lambda. So the faster the saliva is growing, the quicker it will be here. But still, you have two steps from the shift to the adjustment of the size of the sector. That's why, I mean, you have different time scales. One more question. Last one for the talk. So the last data that you show for FIAR, are the promoter. I mean, it's the GFP data. Yes, it's the GFP signal. OK, so do you consider also the maturation time of the GFP? Or do you, I mean, is that important? Here they use fast maturing GFP. So the maturation time was around 10 minutes, which, I mean, it's a time scale that exists. But you see that the oscillation is like two hours. So it's not really impacting the result. Right. Let's thanks the speaker again. And now we have our last talk, I think.