 can anybody hear me? Anyone or everyone hear me? It's perfect. Okay, so I have the pleasure to give him the last talk to wrap up this really nice conference. So for I think most of it was 14 days of learning a lot of new things. And I also had to change my presentation a little bit because of the things I learned during the 14 days, but we'll see how it goes. So my topic is traffic slowdown by antibiotics and my PH mainly, we're mainly interested in how translation limitation can change the cell physiology and how one can model this with non equilibrium traffic models. So let's kind of start from the translation cycle. So I think most of us are familiar, but you have the initiation of the ribosomes on the mRNA and then you have multiple steps that are kind of a lot of times coarse grained, but you have the tRNA binding, you have the peptide bond formation, and then the translocation. And so this gets repeated until you reach the stop codon. Once you get to the stop codon, you have the termination, which then results in a hopefully functional protein, and then you have a recycling step. So now typically a lot of the talks are about chlorinfinical, but they're actually a lot more antibiotics that inhibit different steps. And so for a good starting point it's chlorinfinical though, so this is where I'm going to focus on. So just to clarify, CM is chlorinfinical and it acts on peptide bond formation and also termination. So what is the idea? So this is the kind of plot that we've seen now a lot. And but most talks were mainly about the first growth law and not the second. So we're especially interested in why the second growth law goes up. So in this paper from Diet All in 2016, they measured this really nicely and they measured a lot of elongation rates, but what they also measured was how elongation rate changes with chlorinfinical. And as I showed you before and the chlorinfinical stops the ribosome, so it pauses the ribosome. What's really puzzling for me is once you treat chlorin with chlorinfinical elongation rate actually goes up. And one goal of today is kind of to give you an intuitive and use our model hopefully to convince you that this makes sense. And so the general idea of our model is that you can have antibiotics that bind with a certain rate K plus to the ribosome and then the ribosome enters a pause state. And once it's paused, it unbinds with the rate K minus, which then it resumes elongation. So this type of model has been mainly used to study RNAPs and transcription because RNAP polymerases have been known to pause sometimes. So we use the, so a little bit the traffic model part of it is, Luca gave a great talk on Tuesday introducing this, but you basically have a one-dimensional lattice where particles can enter with a rate alpha and they unidirectionally hop along this lattice with a certain rate epsilon and they obtain the exclusion principle so they can't occupy the same site. So now the adoption of this model is that we, our particles can enter a pause state. So what we effectively do is we induce traffic jams. And I want to clarify a little bit what you see on top. So for me active, when I talk about active particles are the ones that can actually move. Pause particles are the ones that are bound by the antibiotic and the jam particles are then the ones that cannot move and they are because of exclusion principles. So from this we can kind of get the protein synthesis rate and we can also get the density. And here's just a small depiction of what then from an active jammed and paused particle looks like. Just to give you kind of a quick overview of how these things work in different regimes. So on the y-axis we have unpausing rate and on the x-axis we have pausing rate. So the higher you go on the y-axis the faster you unpause. And when you go to the right the faster, the more pausing you have, the more paused particles you have. So if we start with very fast unpausing and not a lot of paused particles we kind of get to the standard Tazeb regime where we really have this nice parabola and we get a nice maximum at a density of one half and for me intuitively this means you have the maximal current when every other particle, every other site is occupied by a particle. So they can really nicely move slowly. So now if you increase the pausing rate you get like a lot of transient short pauses which it looks the same but the y-axis is different. So you kind of rescale it with the elongation rate. Now the bottom right graph, now it gets a little bit worse for the cell let's say or for the protein production because now you decrease the unpausing rate which basically your entire system gets stuck and again the y-axis you have a big decrease. So the most interesting part or where you really start to introduce correlations is in this regime because now when you decrease the pausing rate so you have very rare pauses but if they pause they stay there for a long time this then creates long traffic jams. And one might ask where does chlorinfinical fall into all of this because as you can see the theory really matches up in three regimes and it basically goes all the way to the lower left. So chlorinfinical has really long pausing time and it has also a very low pausing rate. So what I mean by this is that it rarely binds and if it binds it stays there for a long time. Yes please. So there are multiple reasons for this and one reason is because in these, so this formula here on top is basically the standard TASAP and this relies on mean field and mean field you basically say okay we feel a constant, all interactions are kind of constant and so once you introduce really correlations then it kind of all goes down the drain and because we actually have a huge time scale separation there's also something more going on and we'll talk about it on the next slide in a moment. So we, an intern worked, a master's student worked on this but it's work in progress because he left after the, yes. So all the on and off rates are many of orders of magnitude smaller than the elongation rate. Yes. Yes. Many orders of, this is just blowing my mind. So, yes. Yes. And it's, it's, it really is many orders of magnitude different. Because what is the hopping rate? So the hopping rate is depending on where you, what you say 10 amino acids per second. Okay so it's 0.1 per second. So these things are, it takes an hour for this thing to come off once it's bound for several hours for it. Yeah. No, no, no. No. Because I, wait, no hours. Maybe I missed an order of magnitude there. K minus over epsilon is 10 to the minus 4. You 10 to the minus 1 is epsilon. So K minus is 10 to the minus 3. That's 1,000 seconds. Right. It's 20 minutes. Yes. Yes. Okay. So, sorry. Yeah. I might have, I think what I read in the paper was orders of minutes. So I might have screwed up the order of, one order of magnitude here. I have to go, I have to double check. But even in minutes, it's much longer than several minutes. And it takes an order for an, an hour for an antibiotic to find then a, a ribosome to bind. Yes. So the number that I give here, I should have mentioned this is that the, it depends on the curve of a concentration. So you, you have, this is for one micromolar of chlorinfinical. And so you can typically the experience are between 1 and 12. So you would go one order of magnitude up as well. But yes, in general, it's really, you have a big time. One micromolar is one molecule per cell, roughly, right? I don't know. Sure. Even more. Yes. Then why does it take it so long to find the ribosome? If somebody could answer that question, I would love to hear the answer because I, I, I also, to be completely honest here, I also don't quite know how they measure these rates. I took them from the, I took them from the Terry Walsh group from the diet all paper. But yeah, if, if there's any, one, any of this room that, that haven't an idea of all these, I would love to talk to you. Oh yes, yes. So the, the typically a lot of these traffic models, you kind of start with even the simplest model where you have just periodic boundary conditions and your particle go around in a circle and you just set the density. And then there's a mapping between periodic and open boundaries, which you can use. But because of the time scale separation, we, we have a problem and Lorenzo worked on this thing. And we can see that our solution is better than the one given in the literature. But if we, for periodic boundary conditions, but there are a couple of problems for the open boundary conditions, and it's a work in progress. So if anybody wants to dive in the mathematics, I can try to explain to you, but we'll see how far we can go. Okay. So going back to the, to the system and it kind of touches a little bit on Eric's thing. So one thing that comes out of that you have not, that it takes really long to find the ribosome in bind is that you have a lot of ribosomes that can basically finish the trans, translation without being passed. So you have kind of a state where you have normal current. Then one time you get a pass and now you stay there for a really long time. And this then creates traffic jams. And in order for this one letter, so this one mRNA to go back, it has to basically resolve the cluster piece by piece to go back to the, let's say normal state. So this is just for one mRNA molecule. If you do this for mRNA molecules, you kind of get a fraction of active mRNAs and a fraction of bound mRNAs, which gives you the concentration of bound mRNAs. So you add the free ribosome concentration, which kind of determines your initiation rate. And then this gives you the total ribosome concentration. So this is the, then the initiation rate with alpha on times the free ribosome concentration. So the next comment on these orders of time scale degradation probably matters for two reasons just because a degradation of mRNA. One is that it seems to be the common knowledge that you have exposed when you have exposed mRNAs that is typically where RNAs is attack and degrade the mRNAs. And the other one is just the pure timescale of these things. So then if we want to, now we kind of know the protein production. So we can write down how the number of protein changes with time and we can relate the growth rate with the current. One other important ingredient that Hosanna touched on a little bit is the flux balance. So the flux balance, kind of how your metabolic proteins, depending on your nutrients, create precursors with a certain nutrient efficiency new. And these nutrients get incorporated into protein via protein synthesis. So writing this down mathematically just means that you have this influx of nutrients and the outflux of nutrients and they have to be equal to, because you assume balanced growth, the growth rate times the number of precursors. Solving this we can go get to the nutrient efficiency where basically on the bottom it's Phi C, but a lot of times we assume that the Q-sector that Lothanna mentioned is constant, so we can replace things. It's not the most important thing. So we use an ansatz that basically says, okay, we have a certain concentration of tRNA and that gets up-regulated with ribosome fraction. So if you have more ribosomes, you need more tRNA precursors. If we sort of plug this in, we can kind of relate the Phi R to the growth rate. And one thing that I wanted to point out is if you decrease your lambda here, you basically, your Phi R becomes your Phi R max, and that's why you get this slope in the end. Okay, so how do we do this numerically? Oh, yeah, sorry, the justification. So if you look at how long it takes for the ribosome to translate one codon, it is one over epsilon, which is the elongation rate, it's equal to the time it takes the precursors to get there, plus the translocation, which for us is epsilon max. If you rearrange things, you can put it in this nice Mikaela's menten form, and with our ansatz, we get something that looks like this. And then Terry showed this plot last week, I think on Tuesday, and this kind of fits it nicely, but of course it's a fit. So how do we do this? Oh, one thing that I wanted to point out, which I think is really fascinating, that nutrient and translation limitation actually collapse on the same line, if you look at elongation rate and ribosome fraction. So, yeah, again, if anybody has an intuition, please talk to me. So let's start with the numerical approach. So we basically choose our starting condition, so we have a certain Phi R and a certain lambda. We use the Balakrishnan data to set our concentration of mRNAs, which for purpose of the second cross law stays constant. We can get our nutrient condition, and then we can also, with the Phi R and lambda, we can also get our starting initiation rate. And this initiation rate Luca talked about on Tuesday, but we inferred this from the data above. We're using alpha on. So now we kind of need the elongation rate, epsilon as well. And from there, if we know how many, how fast we initiate on the mRNAs and how fast we go, we can, we know the density, so we know the bound ribosomes. With the bound ribosomes, we know the free. And with that, we know the alpha on, which also doesn't, we keep constant from here on out. Okay, so now the cell happy and nice, and so you have these normal pictures. Now you start to introduce antibiotics. And so now antibiotics basically really start, you start to cluster these mRNAs and they kind of soak up the free ribosomes. Right, because you keep your Phi R or your total ribosome concentration the same. And so you suck up your, the ribosomes get stuck on the mRNA, you increase the density. So this changes alpha, because alpha depends on the free ribosome concentration. So we get a new alpha to rerun the simulations again. So we kind of trying to find a numeric, a steady state numerically. We do this until alpha doesn't change anymore. So in a sense we, and the only thing that changes here in this equation is the free ribosome concentration. So as we find numerically a state where the free ribosome concentration doesn't change, we accept it. It just occurred to me with these very long time scales, that essentially what is happening is that most ribosomes make it from initiation to completion without anything happening, then every once in a while one gets hit and it basically blocks that mRNA. And then it's blocked, that mRNA is basically taken out. So is that part of the model that the mRNAs have a certain length and they're degraded? Yes, yes. So we don't consider degradation, we definitely have to. And I think with this the length, we assume it's around 250, that's just an average length. But yes, it's very possible that the length really plays a role in depending how susceptible it is to actually be hit by an antibody to have a pausing. But so now with our new alpha, we get our free ribosome concentration is fixed, we get our new alpha and now because of flux balance, the cell senses with a lot of regulatory mechanism, PPGPP is probably involved, that the flux is imbalanced, so it reallocates its proteome. And so now we have a new proteome, we have a new ribosome concentration, but that also means again that our initiation rate changes again. Because now we have a lot more ribosomes in the system and so we have to rerun this whole thing again. Once alpha doesn't change, we accept it as our new lambda, we accept the new phi r, and then we do this until our proteome and our growth rate doesn't change anymore. So once we get there, we kind of have the first point and we increase our antibiotic concentration from there on out and we get something that looks like this. So I still haven't really talked to you about what happens to the elongation rate with our ansatz right? If phi r goes up, the elongation rate also goes up. What for me is let's call it a little bit more remarkable, and then you choose different initial conditions and you get different things. For me what was also really remarkable about this is that the slope is different. So for poor nutrient conditions you really start to increase, for poor nutrient conditions with low growth rate, you have a really sharp increase and that slope tends to go away a little bit. So just to finish this up, the idea is that if you're in a low growth state you're kind of limited by the arrival of the tRNA, by the precursors to move and for high growth rate you're saturated. So now once you add the antibiotics you really decrease the amount of active particles. So essentially you have more precursors for less ribosomes because also phi r goes up so you also have more precursors. So you have the two effects, you have more precursors and less active ribosomes. That means all the other ribosomes speed up. And with that I would acknowledge my team and if I forgot anyone I'm sorry. Thank you for your attention. Questions? Great talk. I have a question about, have you guys explored the effect of other kinds of antibiotics like tuning the reversibility or K-on-K-off ratio? I love that you asked that question because I just, when I was sitting there I prepared the slide. This is taken from the dye paper and you see here you see different antibiotics. So for tetracycline, eryomycin it kind of works the same. But once you add like acidic acid and you change this phenomena that you, with increasing antibiotic concentration, your translation rate goes up. For moob it's not necessarily so surprising that it's so different because it's inhibit tRNA charging so it doesn't actually bind to the ribosome. For fucitic acid it's weird because it's so chlorinfinical stops the peptide bond formation and fucitic acid stops the translocation of the ribosome. So it's basically the next step which I think in my point of view should be the same. But it's worth checking his head. And essentially in turn it does prevent translocation event as such but it also inhibits by soaking up translocation, elongation factors g that could translocate the ribosomes. Essentially by blocking one it blocks further ones. But wouldn't that then be basically the same mechanism than before? Because you have, you reduce your elongation factors. Not necessarily. Yes, you're affecting the active ones. Exactly. So fucitic acid also interacts with recycling but so you also have this double effect where you stop initiation. That would be also interesting how I think Bohr worked on this with how you have the two effects that you have an antibiotic that act on initiation and elongation and then how this changes. One more question. If they are not let's thank the speaker again.