 So thanks for coming. Thank you. It's great to be here. Looking forward to the workshop of a topic I dearly love. Okay, I should put down this. Nope, huh? Okay, I have my own. So we're talking about physiology. So what is physiology? Physiology is about a whole. The whole could be a cell, could be an organism, or could be a community or a whole. But in the context of this workshop or the division is that I think the physiology referred to the cell, and then we have the larger scale, that's a community. First let me tell you what I will not talk about and some of the negative messages I hope to convey. Once I do not know how many molecular system biologists are out there, but the cell is not just a collection of molecules that interact with each other. Quite often if we talk to molecular biologists, that's the way they view the cell. Yes, certainly molecules are important, interactions are important, but it's not just that. There's more to the whole. To the ecology modelers, we would like to write down a whole bunch of monokinetics and the metabolism excretion and uptake and so forth and talk to each other. Well, yes, that may be a part of it, but it's probably more than that. You shouldn't see the cell just running a bunch of monoequipments, right? And the environment typically is more than just a chemostat. Even if you try to make it a chemostat, often it's more than a chemostat. And then to those that model things from more the evolutionary perspective, or we're often, yes, we would all like to find optimization principles that may exist, but then it's often not clear what these guys hold fixed and what these guys optimize them, even if they're doing optimization, right? So I think it's a very interesting topic to think about to explore. So yes, so we're talking about physiology and the physiology is at the nexus of the linking of molecules and the communities, right? So what's the output of physiological studies? What's about the behavior of the cell? So the output is about behaviors, right? So it could be how fast they grow, how much stuff are made, viability, et cetera, et cetera structure, right? So it's beyond molecular properties. And what's the input? What input is the environment, right? What nutrients are there, temperature, pH, et cetera, et cetera. So what we seek in the physiological study is a direct link from environmental input to the output of the cell. The difficulty is of course that cells are made of molecules and these things really affect molecules, right? So that's really what it is. And we need to somehow, you know, core screen over the molecules to get to a link to physiology. And the best examples that we can point to where this is done successfully is monogross law. This monogross law take as input, concentration of nutrient and output is physiological property. I'll talk a little bit more about monogross, but it's a highly doubtful that anything coherent will come out, you know, treating the cell like a chemical reaction, that's amazing. Okay, right? But then I should remind you that not everything you ask or you look at will be simple, okay? There's only simple things to report if the cell decided to do something to make it simple. Otherwise, no, you're writing down a collection of equations and it does whatever it does. Okay, so now I come from statistical mechanics. Many of you come from statistical mechanics, right? And in statistical mechanics we say, well, we don't care what the cell or whatever the system is doing, we just apply the power of statistic and then we get something, okay? But I'm not sure how successful that approach would be. Okay, because yes, you can get this for some average behavior, right? But often, a living system already in a very special corner of the parameters, let's say, right? And what, well, it's my interesting, one of my interesting looking living system is to see what this special parameter space, where interesting behavior can arise out of this special parameter space. Okay, so, right, so the, so monogrocelar is about nutrients, right? Can we say similar things about temperature, pH and other variables? Do we have to struggle through molecules every time? What about beyond exponential growth? We'll see, I mean, a lot of times in a community, what right do we have to ask to hold the system in exponential growth, okay? And, right, and the other thing is a similarity difference across organisms. Yes, Monod studied E. coli and he found roughly where he varied in nutrient concentration, there's a simple relation, right? Even that is applicable to other systems. What is underlying it that allows it to be applicable, okay? And of course, much for the properties that we'll be talking about today and beyond, what right do we have to expect for them to go beyond model organisms that's carefully studied, right? And sometimes we'll see surprising universe already, right? Sometimes what we expect to be simple is not simple, right? It's just that we have very limited understanding of living systems and our intuition is not a good guy. Okay, so I was asked to give a number of lectures. I'll be giving three lectures and just kind of roughly give you a sort of a game plan for at least my part of this week. Today and the tomorrow's lecture will form a unit, okay? And so today I will be laying down some basic concept, some reviews, right? And some recent advances. And then they'll be gearing up to talk about a topic that we recently have been working on. And I think either this audience only Eli has heard it, okay? And so I think it's a very, well, it's to us, it's very stimulating and stimulating in terms of making, not falling asleep, okay? So I would love to give feedback from you guys, okay? And yeah, so today I will be talking to you about some of these things, the E. coli and with having in mind that tomorrow we'll be looking at what happens to other species, okay? And I won't tell you which changes, which will be the same, right? So you'll have to be on alert. And so then tomorrow afternoon we'll have a group discussion as of all for the mention. I think that'll be fun, just everybody will participate. I mean, we'll toss out a few slides to generate questions and I think with a group of physicists here and just discussion will just take over. And then on Thursday I'll talk about some aspect of a community dynamic, something we've been working on, something we are thinking about and writing up and to get your feedback, okay? So, and as Jacopo was saying, please interrupt me any time because I don't, yeah, this is a physics center, right? I don't feel right otherwise. Okay, so of course I will start with Olymolar, the, I guess the founding father of this field of a microbial physiology. Well, I would say maybe, maybe, one knows the real intellectual founding fathers, but a lot of what we directly work on come from Olymolar. Okay, right, so they were looking at Salmonella in the late fifties, but here data is for E. coli. And if you grow E. coli's in a bunch of a medium, so LB will be up here, some of the acetase, slow growing medium will be down here. And so you get this culture into exponential growth and you measure some of the very simple, the total amount of RNA in the culture, total amount of protein in the culture. Take the ratio, see that they form a linear relation. Okay, and the, so the X axis is the steady state growth rate system and I apologize for historical reason when calling it lambda. Yes, mu is also good. At the time we have mu for something else. I think in the south division field, it's very important that it's a doubling per hour, right? It's a doubling rate and this is specific growth rate. Okay, so this, so as you change nutrient quality we'll have this linear relation and the RNA protein ratio stands, it's a proxy for ribosome concentration. Ribosomes are the machinery that makes proteins, okay? And molar at the time already, Nihar and the magasinic were the first people to actually show this type of a plot, but these data's already containing models in molar study. So they already have a pretty good understanding of where this came from. That is to say if all of the protein in exponential growth for E. coli, most of the protein are stable, okay? The degradation is about maybe 5% or less. And so if all the ribosomes are engaging in protein synthesis, okay, then the rate of a protein accumulation should just be the flux of a protein synthesis by the ribosome, okay? And then it can write down some equation instead of say growth. Growth rate multiplied by the total protein mass of the cell or of the culture, which is per something, that's the rate of accumulation. And the rate of synthesis is how fast the ribosome works multiplied by the number of ribosome per same number of quantities, okay? And now if you write the number of ribosome as a mass of all of the ribosomes in your culture divided by the molecular weight of the ribosome. Here actually the mass of the ribosome of proteins we're just talking about proteins, okay? Then you have a relation like this. If you equate the two together, okay? So then we see the fraction of ribosomal proteins out of all proteins in the system we'll call it phi ribosome, right? It's just growth rate divided by elongation rate in the unit of a mass of ribosome. So this was a way of a rationalized this linear relation, okay? And when we were confronted with this kind of thinking, that's great. But first let's check whether the numbers make sense, right? And so according to this description, the slope or inverse slope of this should be proportional to elongation rate. This is the case. And then with Mad Scott, this is just a study. We look at the ribosomes for mutants of E. coli that have translated different rates. This is a wild type. At least the mutants, okay? These mutants have slower translation rate and the slope increases, okay? And you can actually compare the inverse of slope to the elongation rate others have measured in vitro and you see there is a linear relation, okay? So then this is an experimental way to make this check, okay? So this seems quite reasonable. And okay, but then the question is before I go on, I'll go along this line but I'll say so why should we care, right? So for E. coli, if a lot of post studies. So I would like to give a two example, right? One is the, okay, so ribosome is not the only thing that have a simple relation with the growth rate. And another is a catabolic system. So for example, if you feed E. coli with a lactose then expresses lactation and LACZ and so forth, right? And the, you can do experiments, is through our steady state growths you can reduce the uptake of the cell, reduce the lactose uptake rate, okay? So then it becomes carbon poor and then it increases the expression of the LAC system, okay? In this very simple linear way. And one can go into analysis of where this comes from. Basically there's a symmetry between this and this, okay? And this event going, the error going this way is called catabolic repression. It's a phenomenon known for a hundred years. Okay, it's not just E. coli, but many microorganisms. If you give it better and better carbon source then it reduces more and more expression of a catabolic enzyme that's used to bring in carbon source. Okay? And so this is an example of going the opposite way, but it's the same statement running in reverse, okay? So why should ecologists care about this? Well, this is intimately related. Oh, so the two parameters that determine this line. One is if you extrapolate to zero growth how much of this enzyme be expressed. So this is kind of the basal expression rate in absence of a regulation. This is a produced by a regulation, right? And then there's another number we call the lambda C. That is basically it's reflecting if your carbon uptake is not the problem at all, but you have an infinite carbon coming in, how fast can this cell grow? Because it's not only carbon, it's still need to take in nitrogen and do lots of other things. Okay, so that's the two numbers. So what does it have to do with anything? Well, it has to do with the monogrosal that we talked about, right? So this was a monosynthesis, a page from monosynthesis done in Paris in 1942. You know what was happening in Paris in 1942. Yes, Monod was a resistance leader and he was also doing research. Right, so this is for lactose. So you vary the lactose concentration medium, right? And measure the growth rate. And then something very simplistic behavior that emerges. Okay, so how should we understand this? Well, from a microscopic point of view, you say the growth rate. So rho is a density of cells, right? So then the increase of the number of cells in the culture is given by the uptake of lactose. The lactose converted to biomass, Y is the U. And then the, so this, you can expand it. I'd say if the enzyme that takes up lactose has a, can be described by mechanism and kinetics, right? So then this will be the lactose dependence. And then you multiply by the enzyme concentration as expressed, multiplied by the cell density, then you get the uptake of the entire cell, right? So that's the first layer view of the system. So often, when it stops here, say, ah, that's where monokinetics come from. But that's not the case, right? Because of this here. Monokinetic, this is describing steady-state exponentially-growing cells, okay? Adaptive cells. And adapted cells, the enzyme concentration change. So in fact, you should be looking, you should be inserting this enzyme concentration by this grocery-dependent. And so when you do that, you get something, or whatever you get, right? So it's a more complicated system, but then it turns out that if you simplify it, you still get a inverse relation between inverse lambda and inverse lag. So this is still effectively a calculus relation, okay? And of course, then this you re-aridered, you're getting to this form with the effective parameters, okay, that depends on two things. This combination is a property of the enzyme, right? And then this lambda c is the property of the cell, okay? So even in the monokinetics, right, you have a meeting of the property of the entire cell. So the cell there, the property of the cell is there, okay? And so you may ask, well, how do these numbers compare to each other, right? For the lag system. Anybody know? The answer is written, it's already in this formula, okay? So the lambda zero here is the saturated grocery in the saturated limit, like infinite batch culture grocery, okay? Lambda c is this best speed limit of growth for different carbon sources, okay? So then to see the magnitude of this, you just need to compare the lambda zero to lambda c, right? So lambda c is here, it's no single substrate can reach that number, okay, it's a speed limit, right? So just ask yourself where, what's the grocery of E. coli and lactose, right? If it is here, so lactose, this is actually lactose, okay? Then you see it is very close to lambda c, that means it's saturated by properties of the cell. It's limited by properties of the cell, okay? If you change to a different carbon-sauce mannose, it is up here, then it's limited by the answer, okay? So, yes, no, this is a concentrate, sorry, this isn't some arbitrary unit, you need to be converted to concentration, sorry. I just took, I just took it out of the, yes, it's not, you can convert this to concentration or the total protein, how much it is, then the dismemberment would match, yeah, okay? Right, so, yeah, so this is a very simple lesson, right, to see that, yeah, in monoconundix, it contains the property of the cell, right? And then you can ask, well, what happens when nitrogen source change, for example? Well, when you change the nitrogen source, then this lambda c is changed, so depending on where you are, okay, then you get different results. Okay, so then, yeah, so this lactose grocery is here, so for lactose, it's limited by other. So, yeah, if you reduce the nitrogen sources, lambda c will shift down, okay, and then everything will shift. Okay, so that was for a minimal median with a simple carbon source, then we can also look at what happens in rich median, where there's often a situation when the bacteria are often in famine or feasts, and during feasts, all kinds of goodies are there, right? So this is an example where for E. coli, we feed it with glucose, that's a gray bar, and you can add various goodies, so CAA is just a suite of amino acid, hydrolyzed product of Cassie, and then RDM is a rich-defying medium, where you also provide nucleotide, vitamins, and such, okay, and the grocery keep on increasing, right? Then you see this linear relation, so this is now ribosome content measured in amount of ribosomal proteins per total protein, so that was the phi RBI was speaking of, right? So it keep on increasing, okay? So this is the glucose minimal median, one of the fastest carbon source in minimal median, and then you give it a supplement that keep on increasing, okay, and this is in absolute units 25% and up to 40%. This is not just, sorry, this is not just the ribosome but includes elongation factors and other stuff that's used to escort the ribosome. Okay, so you see that between glucose minimal median and rich-defying median plus glucose, one of the best defined rich median, there's a 15% increase in the protein allocated to ribosome, and that's just basically the, given how fast ribosome is going to grow that much faster, you just need to have more ribosome, okay? And where does 15% come from? And shown here are some of the other protein groups, so in this paper we have a list of, it doesn't go so, and most of this 15% just come from reduction in amino acid biosynthesis, okay? So when cells growing in the presence of amino acid, it basically suppresses all of the synthesis of amino acid, okay? And that's about 15%, right? Now, there's a consequence to this and the consequence is that the, if you're going happily in rich-medium, then suddenly amino acids are gone, right? And then you have to grow in minimal-medium and then you have to make all the amino acid, okay? And so if you make a shift experiment, say you would first grow your amino acid plus this carbon source and then take away the amino acid, only leave with the carbon source. So carbon source hasn't changed at all, okay? Just amino acid's gone. Then it has a two hour life. It doesn't matter what kind of a carbon source you give it. All right, so these various kind of ingredients could play a role. This is not what we normally call dioxy shift, but it's a similar, there's a similar idea. All right, okay, are there any questions? Feel free to ask some questions. Yes, then, up and down? Yeah, so this is, so as I said, so these two are without the carbon supplements and the faster two groceries are with the carbon supplements, okay? And then you see like nucleotide synthesis, you see the up and down because it's only this guy and then this guy have the nucleotide supplement. So with nucleotide, of course, it's a surprise, yeah. So it's more complicated when you dial grocery, you cannot just dial when it comes to rich media. It depends on what you give it. So let me come back to this simple linear relation or we'll be dwelling on it for a while, right? So this is the now, actually, just take the ribosomal protein, add up all the ribosomal protein and divide by the total protein. So the percent of the protein, that's the ribosomal protein, right? And that can be converted to number of ribosomes. And that was the same data I showed you. We call this the R-line, right? And so, which is, phenomenologically, you could just write down a relation like this, grocery, phi Rb is y-axis, this is a slope. We call it inverse, the slope is something that's more interpretable called gamma Nr. And then there's offset phi Rb, two parameters, okay? How should they be related molecularly to what we know? So we already said the, this is, okay, right? So I already mentioned, if we assume efficient translation, every ribosome is engaging translation, then we get this relation, okay? Where this epsilon is the elongation rate in units of a massive ribosome. And further I showed you that we directly tested and we find that inverse slope is proportional to the elongation rate, right? So, is this enough to say that this inverse slope is this quantity, right? So now we're talking about with equality, right? And, well, actually, not quite, okay? And the reason is that if you measure the translation rate, you actually see a two-fold change between the slowest grocery and the fastest grocery, right? So, okay, so that was something that was first done by Hans Brammer in 1976. So Mora has all of this idea, explanation in terms of what we're saying here, right? That the, sorry, my thing is now working. So we have this, so Mora was thinking along this line, so there's a ribosome that's translating some rate, right? And so things are allocating a resource in this way. Then, Hans Brammer produced this data. He actually measured the elongation rate, okay? So he did the three, four points, and it's clear that already it's not constant, okay? And that basically completely killed this idea, okay? And that was done in 1976. Mora died in 1979. I don't think he ever forgives Hans for that. Well, nothing to forgive him, it's just the way it is, okay, and I was told he was not happy. The last several years of his life, okay? So, yeah, so something like, sounds very good, right? But kind of, it's where you actually do the measurement, it's just, it's not there. And have a factor of two change, right? So then, I certainly cannot put the equality here, I mean, with which elongation that we talked. Okay, so then the next thing to try is, so we tried this a little later, that is the, we said, okay, so let's say, okay, so fine, elongation rate is not a constant, but it's a function of a grocery, right? But let's suppose it's a function of grocery, then let's just put these two equations together and see what we get, right? And when you do that, you get another mechanical relation, okay? You get the mechanical relation between elongation rate and that grocery. And then the, so from this, it's tempting to say that, okay, this is obviously have to do with the, no, this is a saturation when grocery is infinity, whatever the saturate to, we call this the E max, right? And then this suggests that we should interpret gamma, this inverse slope as the maximum elongation rate, okay? And if you plug in a number, they even look quite good. Okay, so we know what this number is. We know this is slope and they correspond to each other. I'll show you in a minute, okay? So it works well for fast growth, but clearly for slow growth, it's just completely wrong. It's nonsense, right? Because at slow growth, a grocery approaches zero, right? We know that the elongation rate approaches about half of the maximum elongation rate. So it's still elongating quite a bit. You can measure it. But ribosome, well, ribosome also goes to a finite, right? So there's no way, you know, this is going to zero. There's no way this equation can hold, right? So something's wrong, yeah. No, no, this is just data, yeah, yeah, yeah, yeah. So there's, yeah, so there's some, yes. There's some slope, but the point here is that zero growth is finite, right? There's no way to get around it. You have lots of ribosomes sitting there and you can measure how fast they elongate it, okay? And there's no way it's producing zero growth rate, okay? And so, of course, then one important ingredients is some or most of these ribosomes are inactive, right? So there are lots of molecular studies on what factors cells express as slow growth to inhibit, to make, to hold ribosome inactive, okay? So, but we have no idea how to set the level of inactive ribosomes. I mean, we can look into regulation, but finding binding constants and that, and then this is not getting closer to explaining, right? So what we have is a missing parameter here offset, but to explain that, we have to bring a lot of molecular details so this is not the productive approach, okay? But it does show that to this simple offset here, there's important biology, right? And the cell cares about it. And to a mathematician looking at this, I had to see some number, right? It's a number that cell cares about. In a sense, that special mechanism developed to put it. Yes, Tom? Yeah, so we're, let's say, at zero plus. We're, let's say, 24-hour doubling, okay? It's simple to put in some mediums growing very slowly, okay? And yeah, so you know how fast there'll be protein synthesis on the whole, right? And there's nothing compared to the amount of ribosome ultraviolet radiation, right? So, so to me, no, there could be many things going on, including protein degradation and such, okay? But that one important aspect is inactive ribosomes. Okay, so the, so we don't know what to do, okay? And so I'm gonna come back to this in five, 10 minutes. What, how much time do I have? Am I already done? I have half an hour, okay, okay. I'm doing a question. Huh? I'm doing a question. Yeah, yeah, yeah, yeah, yeah, okay, yeah. Okay, so then I'm gonna switch the gear, I'll quickly leave you with this question, okay? But then the answer to this sort of came about accidentally in a different study, which is also related. So I'm gonna tell you this a different study and then come back to this, okay? And the difference study was motivated by many tough questions we had, like already with the paper with Matt Scott reporting these gross dependencies and effect on the cell. And so we had a, so I guess at any time you put out something, you get criticism from all kinds of people, but our strongest criticism of being actually being from physicists or maybe biologists don't say anything when they don't like it, okay, but physicists will actually tell you, right? And even some of my most respected physicists are not doing biology, right? And the criticism is, what are you saying? The X axis is a growth rate, right? I mean, growth rate is regulating this, growth rate is regulating that, right? So it makes no sense, okay, basically. And so we presented that study as a phenomenological study, we don't know why, right? Just called a bunch of correlations, but of course the question is always in mind about obviously cells are organizing this response in a quite reasonable way according to growth rate. We can at least very mildly change the way you grow these cells with different carbon source and so forth, it doesn't matter, right? So cells have a way to know about growth rate, right? But how does a cell know how fast it grows? So this has to do with a perception issue, right? So now we're talking about cell, the bag of molecules, but how does a bag of molecules know how fast it grows? And okay, we can ask the same kind of question that these days we're studying community and ask the same for the community, right? The community is doing something. How do members of community know what the whole is doing? Okay, until, and so on Thursday, just a minute, I'm gonna present something that assume that the community knows what the community, the state of community is, right? And can you imagine immediately people have the same kind of objection for, well, how does it know? People, even though we're physicists here, we've been trained by biologists to challenge these things about mechanisms, right? Until we have a mechanism, how should we believe in this? So in this case, yeah, so Mako now. So you could say, right, that the cell senses the temperature, so they can sense, right? It can sense the concentration of lactose, or probably not, because I mean, only outside can you sense the concentration of lactose, but we've done an experiment, we've played with the lactose uptake, so lactose concentration is actually high, right? We just limited the uptake of lactose. It does behave exactly in the way as if it's a reduced growth, right? So cells probably smarter than just kind of a, making a kind of a fixed mapping of what the environment is to the other. And you can also imagine, I can give a combination of nutrients that has no chance of seeing before, and it will still work in problem. So it has a smarter way to figure out how to solve it. So that's a... Let's say, for example, charged RNAs. Right, so you can think about, you can think about very, you can think about flux of this, but then immediately the issue is, let's say if I have a multiple flux coming, which one should you pay attention to? Okay, so if you ask this question to biologists, to biologists, immediately they'll tell you about this special molecule, PPGPP, right? Ah, this is involved, it's known, right? It's involved in growth rate, mediating growth-dependent response. And what does PPGPP do? Well, then they will tell you why my control is not working, right? So it listens to tRNA charging, right? So here's a reminder of a translation process where tRNA charge tRNA, so the system that charges tRNA and the charge tRNA is affecting to the ribosome, okay? And so PPGPP is kind of a survey sum stepping in here to see how the translation process is going, but then you have the similar kind of a question. I have 20 amino acids, which one should you pay attention to? So it's never mind about PPGPP, how would you design a system, right? You have many, many things that's coming in, you know, you have Italy, right? I mean, the economy of Italy, why should you monitor it to see the state of growth in the economy, right? So it's a real economical question, okay? How to monitor it. And clearly, if you know something about how far this should be growing, right? You are growing, it's a good thing. So you can plant these accordingly. So we did this study, and then the upside of this study is that actually PPGPP senses the elongation speed of the ribosome, okay? And but they're just briefly walk you through this and to see what's the strategy. So we have some piece of data and with data with some imagination and then there's a picture that suggests how the cell might be sensing it, okay? So here's an experiment. This is a typical dioxy shift, a growing glucose and the glucose run out and it switches to glycerol and during this shift there's a lag because the cell has to make proteins to take up glycerol, okay? And during this lag, there's a period where obviously growth rate is changing and then we can do measurements, okay? And so we measure the elongation speed at various point during the lag and this is very laborious study, right? At every point it takes on both and the elongation speed measurement and there's a dip, growth slows down and it slows down and then gradually recover by the time an hour, okay? We also measure the PPGPP level, okay? And it has the exact opposite behavior. And we make a scatterplot of the two. You see a linear relation between the PPGPP level and the inverse of the elongation rate, all right? And so we call the, so there's a nice extrapolation down to sort of a zero PPGPP which would be like the fastest elongation rate possible and we call this the inverse of a maximum elongation rate. So this is defined for the maximum elongation rate, okay? And so this study was done in transient but we also did it in steady state, okay? So study scores are changing the carbon source and so forth and then these are the color symbols, okay? And this data, this line here is the blue symbol and they lay on top of each other. So both for transient and for steady state is the same relation between PPGPP level and the inverse of the elongation rate, okay? So then this data and with this data then we attempted to write down such a relation. Yeah, yeah, so what we directly measure is the time it takes to produce certain protein, okay? And usually that's kind of the, so the process could be faster because if you measure, let's say you wait, okay, you, so during the transition, you induce a gene expression and you say that takes two minutes to make this protein, in this case laxie, okay? So if you assume it starts from the beginning and makes two minutes, well that gives you elongation speed but in reality there could be a startup time and so forth so be a bit faster but we tried out to the best of our ability to take into account of these startup time, okay? But still we could be missing something, okay? So this is the assumption, the, okay? So then the, so now, so this is all, this is the experimental basis of taking an inverse relation between the PBGPP level and the inverse elongation rate, okay? Now we are putting into some biological facts that the PBGPP is known to repress the synthesis ribosome, okay? And so then you, so there's some data here, this is the RNA protein ratio, the proxy for ribosomal protein, we will also directly measure ribosomal protein, is the linear function of the inverse of the PBGPP, okay? So then we write down something like this. It is also known that PBGPP, when PBGPP level is high, the various ribosome remodeling factors are synthesized and the effect is to titrate away ribosomes. And we were able to, we have proteomic data on a number of these, okay? They are increased with a ribosome PBGPP level, right? And we just write here some together, something that's proportional to G, okay? This is certainly not, I mean, then you can argue about this intercept or something, put an intercept result does not change that much, okay? So we just go with the same thing, yeah? Relative, what does relative PBGPP concentration mean relative to what? Okay, so it's just, so we measure PBGPP by a radioactivity, okay? So it's just a count of a radioactivity. That's the unit, it's measured, so it doesn't mean anything, so we, operationally, we reference this to say steady state glucose condition, okay, but theoretically a better measure would be what it would be in the infinite slow growth condition, but it's just some unit, okay? It's not important for this thing. All right, so then with these two, we're gonna combine them, right? So the active ribosome is the difference between these two components, okay? And okay, so then we say, well, okay, then gross rate is the, just the elongation rate in units of ribosome multiplied by the active ribosome. Now, we have the, okay, and this is just basically a combination of these two terms, so this active ribosome is function of G, but then this E is a function of G also, if we invert it, okay, this inversion we can always, we can only do in steady state growth, right? So this theory only applies to steady state, yeah. PPP is a transcriptional activator, sorry, of these ribosome sequestering genes. Molecular, that's well known, yeah. And that's well known, or is, yeah, okay. Not the, not this, not the relationships, but the transcriptional regulation is, but yeah, yeah, but the PPP is through the SKN and so forth, how it, the KSA. The KSA, yeah. Unless it's too deep of a rabbit hole, does how do those ribosome sequestering genes work? Do they just start being translated and get stuck somehow, or what is the mechanism? I mean, the ribosome sequestering genes, what, how do they work? How do they sequester ribosome? They go and, say, block the site where ribosome will be taking in, in the mRNA and so forth, that's one way, okay. Another way is they actually take two ribosome together, bind them together, okay. So they're very dedicated and very important. If you get rid of them, they're in trouble, okay, mainly in stationary phase, okay, yeah, but yeah. In your experiment, then there is a transcriptional time scale for the activation of these ribosome sequestration proteins. Yes, yes, yes. And then that would, that would actually... We have looked at the minutes. I mean, these things, the very small protein. They're very quick. The very small protein, and it's just like, just turns, that's all they make. I mean, one of the most highly expressed stuff, yeah. So you say that this theory just applied on steady state, but which part does not apply during shift? Okay, so the steady state is a simple way for me to think about, okay. So like, this is a relation we get, right. We know we're varying elongation speed because we're changing neutral, okay. But then inverting this, I mean, I don't even know what that means. So in steady state, I can do this because I know just one to one relation. So mechanistically, I mean, we'll talk about dynamics later, but maybe not. But we do have a piece of work, several pieces of work on the dynamics. So you can use this relation and do the dynamics. But steady state is easy to input. All right, so you see, okay, now, you see the elongation rate is related to PBGVP and the active translating wrap-up zone related to PBGVP, product of two gives a gross rate. So that defines a unique relation between PBGVP and the gross rate. Okay, so that's, we believe that the strategy in principle, details may be more complicated, but if I have a, so gross rate is a product or active ribosome and how fast they work. If I've got my hands on both of these quantities, well, then I have a mapping between PBGVP and the gross rate, right. So now then I can use PBGVP to regulate whole bunch of other things. And the output is to have a gross rate dependent regulation. Yeah, so yeah, so in steady state it's a constant, right? But because of this, because of this relation, when we have to see that what changes at different gross rate, how things change in the connected, so that's a part, I don't think I'll ever get to in this, but I will get talking private. Okay, I'll talk about that, that I'll talk about, right? But you already see that for this to work, elongation rate has to change, right? So more or less picture with constant elongation rate, if it's constant elongation rate, you simply cannot exploit that information. That would not be a productive end. All right, so let me now discuss the prediction of this. Okay, so, but the first point now, I have three parameters here, right? So I need to say something about, ultimately I would like to see the ribosome protein ratio, this R line, the R line should come out of this, right? But then I have a number of parameters, okay? But this can be so easy to fix these parameters. So first of all, gross rate go to zero, and for simplicity, let me just set the unit of G to be one, in the limit of gross rate go to zero. It could be anything, it doesn't matter, okay? Just call it something one, okay? So with gross rate go to zero, obviously the active ribosome fraction need to go to zero, because the elongation rate is now zero, right? So that means, so active ribosome go to zero, that means A over G equal to B times G, right? And I also know that ribosome fraction goes to this offset. Okay, so that already takes care of two constants, A and B. And yeah, so we'll have this relation. And the, so now I can express G in terms of ribosome, okay? The, because I'm working towards getting, expressing gross rate in terms of ribosome content only, right? But then I also, I still have this elongation factor, but when gross rate go to zero, elongation factor go to a constant. Okay, so that constant is gonna set this number C, right? And, but then, so I need to say something about a constant, and here say, well, I know empirically it's a half of the maximum gross rate. Then that fixes everything, okay? So now elongation rate is also a simple function of a G, okay? And then you substitute in what the G is in terms of a ribosome. You have this expression, which is a macalus dependence, okay? So elongation rate has a macalus dependent on the ribosome fraction. And that was actually observed empirically a couple of years before this work, okay? So then we didn't know where that came from, but then, so here it just naturally emerges. And the, by the way, in this macalus relation, the macalus constant is just this offset phi rb zero because, right, so we needed the elongation rate when gross rate go to zero, this two equals elongation rate is one half. So there's no additional parameters. Okay, so now I have everything. Gross rate is product listing, and I know how each of these depends on G and then the G can be inverted to ribosome fraction. And if you work out the arithmetic, you get back this linear relation with the slope, inverse slope now being this, what Moeller was proposing from very beginning but with the maximum elongation rate, okay? And moreover, you can look at the elongation rate as function of a gross rate, the gross dependent elongation rate because you just plug this relation into the macalus relation, okay? And so it has a hyperbolic relation dropping two and a half where gross rate go to zero, and this is the data. Okay, so then, so to check, so this is the output of this picture, right? And so we can check it this way. So we first have the ribosome, the R line. From the R line, we have a two fitting parameter we can extract, these fitting parameters, okay? And then with this interpretation can be used to calculate a maximum elongation rate. And now this is completely, this formula is completely fixed and the black line is just a drawing of this formula without any fitting parameter, okay, so it matches. Or you can fit through this line and go back and look at the slope. So I have two questions. One is about the factor of two, which is kind of magic. And the other one is what I said before, like in this dietal study, you showed a deviation from this linearity, but now we have to think that it's a straight line. So if it's a factor of two, in general, this is nonlinear relation because you have all kinds of nonindependence. If this is a factor of two, it's exactly linear, then you can exactly linear relation, okay? And this is a fit, just dietal has many more data points. So this is a fit, assuming it's a fit to a linear form. So here we are not seeing the same data as in dietal. We are not seeing the slope. So dietal, there was no proteomic data. Yeah, it was, I would say, our first generation proteomic data, which is, yeah, yeah. So we shouldn't trust the data. So at that point, we just sort of were interested in form. We were, we did not think our data was good enough or quantitative, looking at the coefficient. So we should look at the last generation data. The last generation data. The last generation data. Yeah, we calibrated with riboseed. No, because to do this kind of thing, you really need to have a good handle on the absolute concentration. So we should think that this is really a straight line in the data. So dietal was RNA protein. Yes. So RNA protein to ribosome fraction, there's still a conversion. So RNA protein and ribosome protein fraction. Yeah, there's no DNA as well. At slow growth are not exactly the same. Okay. So, yes, the, okay, so we have really a quantitative congruence down to the shifts in the slope and all that. Okay. And yeah, so then all of this I was saying, hinges on this factor two being exactly a factor two. It's a very interesting question I'll return to later. So one more thing you wanna mention is that here's another way to express the gross range. So it's one way is this way, but I can write this factor as a total amount of ribosome multiplied by the fraction of active ribosome, right? There's another way to write it. So it's useful to know whether it's fraction of active ribosome is, okay? So since I told you what these all depends on, the inactive ribosome fraction depends on G and therefore depends on ribosome fraction. And then you see it has this ratio one minus offset divided by the amount of ribosome squared. And then the square makes things, make life quite easy, right? Because roughly, you know, suppose I'm already say three times away from an offset, then I'm only making 10% error if I forget about inactive ribosome. So this expression that Mohler had, Mohler and the 900 and so forth had from the very beginning, actually it's really quite good as long as we are, let's say, for anything in the rich medium, it will well above three fold. But just that elongation rate is not constant. So all of this is basically a footnote to the thing is that basic and Mohler's picture is a correct, okay? But there's some detail that's a, but make it correct even when elongation rate is a grocery dependent. That's a, I think for me it's a lesson between phonological study and microscopic study. This is something in physics, we learn this over and over again, but we forget every time we get it to it, right? Phonological study, it's a phonological study. And if you want to pin down to mechanism until you know everything, you can easily point to a piece of mechanism, oh, something is now working, right? And it doesn't mean the phonology is wrong. Right, so inactive ribosome is negligible in rich medium and this will be important when we talk about the things tomorrow, because we're serving other species who cannot afford to do this kind of measurement in every case. And we can estimate the maximum elongation rate just using the elongation rate in rich medium, okay? So as I said, tomorrow we'll be talking about this in the context of other bacteria, but maybe here I can already ask you guys, right? So we'll talk about a number of features, right? Which you think about, which one you think will be preserved across bacteria? Which one will be species dependent? Any guess? I mean, what's important, right? The what? Yes, master ribosome within 10% of all the same. Yes, okay, okay, that doesn't count. Yes, the factor two is very important. It keeps the factor two, okay? What else? What about the values? I mean, I'm gonna tell you, it's gonna be linear relation, right? And then the only two parameters, one is the slope, one is the offset, right? What do you think is more important about the material care about? The slope or the offset? Okay, so you think slope is not important. But slope has an interpretation of elongation speed of a kinetics ribosome, which is very important, okay? What about the offset? Then maybe there are other biological processes like balancing degradation or whatever else. But what happens as a slope grows and nothing, but here the offset is defined as that you measure with a reasonable growth rate down to 0.1, 0.2 and extrapolate it, so there's a, right, so even for them, there's a meaning of what the offset is. That's right, okay. Why do you need to inactivate ribosomes at all? What is the evolutionary purpose of keeping ribosomes inactive? Suppose at very slow growth, you dial yourself down to very low ribosome, right? Now suddenly, good nutrient come back. You cannot be universal, right? You cannot catch it because you have ribosome. But that immediately answers that this offset cannot be super universal because some bacteria are really bad hedging against bad times, others don't care. They are always growing in a super rich medium somehow and... It will be lifestyle dependent. So the offset will be dependent on the lifestyle and the range of growth rates they want to explore. Right, so keep this thing in mind, okay? I'm not gonna tell you, but tomorrow we'll see what's the same, what's different. And you'll learn something from what they keep the same. So will you say something about how PPGPP senses the elongation rate? What mechanism might exist? Aren't you replacing the growth rate with the elongation rate? I wasn't going to talk about it, but the slides are there. Am I out of time already? Okay, I can get to... I can get to... I thought only molecular biologists will ask these questions, but yeah. So, right, so this is the expression we have. So this is just a phenomenological relation, right? Between PPGPP and the elongation that I talked about. Okay, so then to interpret this, what does the right hand side mean, the ratio of these two, right? Let's consider a step in the translation cycle. We have the ribosome sitting here looking at the tripler codon, waiting for Tion A to come in and it finds the right charge Tion A comes in and then it charges, right? And so this is a time dwelling time. So it's waiting for the right charge to come. And then once the right Tion A comes, then it would shift the peptide bond and then move forward. So we call this the translocation time. So roughly, you think of these two steps in the translation process. Every step takes these two steps. And right, so then the inverse of the elongation rate is just the total wait time. That's the sum of these two times, okay? And the fastest possible, so that the translocation times are obligatory. I mean, you always, okay? So if you have infinite U-turn, then the best you can do is set the dwelling time to zero. Right, and that would be the inverse of the maximum elongation rate, okay? So then this quantity in the parentheses is just the ratio of the dwelling time to translocation time, okay? So if this expression is correct, well then one way to get it is by looking at the ratio of these two times, okay? And at the, right? Okay, so now I can think about this process. You have a population of ribosome, the two population of ribosome that's in the waiting for the T-r-n-a to hit and the one with the charge T-r-n-a, right? And so then if you have a set of flux balance between these two, right? Then you have the product of these two rates to be the same. The amount, multiply the rates going forward with the dwelling time and the amount of the other, by the inverse of the translocation time, right? Okay, so then and the total active ribosome is some of these two populations, okay? So now then you can write down expression for the charging time and then the charge portion that's just the total multiply the ratio of the two translocation time divide by the total waiting time, okay? And then, well, anyway, why am I saying all that to say? So you can sum over all of the population. The first line is for T-r-n-a specific flux balance and then if you sum over all of the pools and you get the relation between the total pools of ribosome sitting there waiting for T-r-n-a in the ones that's ready to do the translocation, okay? So then all that's saying is then this PBGVP, now this ratio can be written as a ratio of these two pools, okay? And so that's another question we're trying to solve. How can you design something to measure the ratio of these two pools? Okay, so you can see, when I think about a model of PBGVP dynamics is the synthesis and there's a degradation, right? So this level would be given by the ratio of the synthesis and the degradation. So the simplest scenario would be if you have a synthesis that's proportional to one pool and the degradation that's proportional to another pool, okay? And so then, so now a couple to what's known molecularly, it is known that the rail A, the molecule, one of the two molecules that synthesizes the PBGVP from GDP, right? It actually does its job when it is in D, when there's a tRNA in the ribosome and it's stuck in the ribosome, okay? So basically, so this is the way we view it is that this is nature's mechanism of probing this pool of a ribosome that's waiting. Because when you're waiting, until you have the right thing to come in, you have an uncharged tRNA to come in, okay? So this thing only does its job, make PBGVP when you have uncharged tRNA in the ribosome, okay? Yeah, and it is even, let's see, I may have a, yeah, so here is the molecular picture, okay? So here's the ribosome, you have the three tRNA. This is the uncharged by design, this last triplet, there's not a charging, okay? So it's an uncharged tRNA that's trapped in it. And sitting behind this is the rail A, okay? And then this is the business domain of the rail A that's where it produces the PBGVP, okay? So the molecules are designed so that the rail A molecule is hybridized with a tRNA, okay? And it gets dragged in, okay? So if it's uncharged tRNA, okay, then the position is switched, the position is different and it basically opens up the only inside of the ribosome that this structure gets opened up. Otherwise, this is a titrated, it's a sequestered by the protein, okay? When it gets dragged into the ribosome, it gets stretched out and that is when it puts in the PBGVP. So it's a very delicate mechanism, right? This is, so there's another molecule that also makes PBGVP, nobody knows about how it works, but here is an example of how things might work. So the final thing is, yeah, so then there is, so this is a biosynthesis and there's also a degradation. That's done, there's only one protein that in E. coli can do the job, Spolt T, okay? Nobody knows how Spolt T works, but our hypothesis is that some signal is, when the thing is ready to move forward, there's some signal that enables Spolt T to do the job. So that way it can sense both the degradation and the synthesis. So both, yeah, these two pools. I'll take the ratio. Yeah, okay. Yeah, so, yeah, I was going to talk about the kinetics. So once we have the causal relationship of how nutrient change changes elongation rate and changes PBGVP, then in principle, the whole thing into work to talk about kinetics during growth transition, actually what happens, right? People in the ecology community just use mono form and just nutrient change and it's sort of, that's what that's, but that's not a kinetics, right? Because mono, the mono kinetics is really not kinetics. It's a steady state relation between growth rate and the nutrient, right? But if you want to talk about kinetics, you have to do this kind of a thing. Okay. Thank you very much.