 All right, there we go. All right, so let me take you back to where we were yesterday. Yesterday we were talking, we spent quite a good deal of time talking about this age distribution. The idea was that the experiments that we'd seen previously, the experiments that we'd seen previously were population average. And it's going to be important, and I'll show you why, in a moment, that we have some sense of what that probability over which we're averaging looks like. And some way, if we can, to deconvolve these experimental results from this averaging over the population. And so I'll tell you about that in a second. What I'm looking toward is explaining if we can these experiments by molar that were now, at the time that I'm about to talk about, a decade in the past. So these are from 1958. The experiments that we'll talk about today are from 1968. And just to remind you, the idea was that the faster cells grow, the faster the bacteria grow, the more mass per cell they have, that is to say, the bigger they are, and the more DNA per cell they have. And that's puzzling, as you say. We want to resolve that puzzle. So where is that DNA coming from? And in second of all, maybe not why are they bigger, but why is this scale here one doubling per hour? And why is that a characteristic time? OK, well, let me pause. Any questions about what we did last time? OK, one other piece of administration, periodically through the lectures, people have asked questions that I've deferred. Like for example, what's the average age of a cell? I think somebody asked. So I've put papers onto that website that hopefully address those questions. And so there's a paper that addresses a question, what if we don't have a delta distributed doubling time? There's a paper that addresses, do cells age, do bacteria age? And there was another question that is, can we experimentally ascertain what distribution we should give for the doubling time? That's also on the page. If you have any other questions, ask me as we go, ask me after the lectures, and I'll post relevant literature if you want to go deeper or farther, OK? All right, so then maybe I'll pause here. Yeah, could you say one more time? No. And that's because they're immortal. So the question is, is there another way to define age? And there could be, right? There could be, what would you call it? This would be the age relative to the bacteria. And then there could be age relative to the laboratory. Like these are four days old or something like that. But because these are in balanced exponential growth, they're sort of outside of time. The only time that matters is their time between birth and division, if that makes sense. And so this comes back to a question you asked, I think two lectures ago, which is, do the mother, or is there any noticeable difference between, say, the great-grandmother and the progeny of these cells? And for E. coli, none that we can tell. They're immortal. It's strange. I mean, from our point of view, it's humans. Yeah, yeah. So can you trace back? Can you say, if I gave you this cell and this cell, could you tell me which one was the grandmother? No. They're totally the same. It just happens that in the laboratory time, one came before the other. But chemically identical. Oh, we have to be careful, though. This is not a laboratory time. So this is, say, the experiment would only take maybe six hours. So there's no evolution or anything working on this. They're genetically identical to the zeroth order approximation. And so that allows you to say, that's what I'm using to tell you that they're indistinguishable. If you let these guys evolve for hundreds of years or something like that, then you can tell just from the genetic drift you could order them in terms of their genealogy, if that makes sense. So they were breaking outside of species rather than just looking at progeny, grandmother, mother, daughter. I don't know if I did. Was that? Yeah? Good. Any other questions? So what I want to talk about today is, like I say, basically DNA replication. So it's not obvious that that's all tied together, but that's where we're headed. And what I really like about this experiment is that it's, again, it's very much like a mathematical proof. You have tiny steps that at each point take a little bit of thinking, but don't break your brain. But then at the end, you end up with something that's absolutely incredible. It's like a proof by our comedies or something, except it's an experiment. And you say, how in the devil did he ever think this up? But this is Helmstetter. And then Cooper as well, although Helmstetter is the originator of the experiment that I'm about to talk about. This is Helmstetter 1968, and Cooper as well, who is his co-pilot. All right, and so the idea is if we could synchronize these cells, we would take this age distribution, which is this sort of exponential, if you like, distributed across the possible ages of our bacteria. And again, there are more newborns in our cells about to divide. And if we were going to synchronize, we would somehow chemically or biologically force this distribution to narrow. So we would turn this into some delta distribution. It turns out for bacteria, that's seemingly impossible. All right, but the next best thing, this is very difficult, let's not say impossible. No one has ever done it before. The next best thing to sample a narrow strip. And so instead of making a delta distribution, you just take a very tiny piece of the distribution. So something like this. And then you know that all the cells in that strip have the same age. OK, so you don't sample them in age. You sample them in time, if you like. Yeah? Can you look at the skews and make sure that you feel everybody's ready? I think on paper that would work, right? And for eukaryotic cells, it's much easier because they have checkpoints. And so these guys are everything simultaneous. And so you would have to have some kind of very accurate killing mechanism that's cued to something that's not a checkpoint. I mean, it would be something, oh, I mean, you could, but that's a little bit sloppier. But you would have to cue it to, say, kill the cells at some certain point of replication in DNA or something, or no, allow those to survive. So we're going to do something similar here. What's going to happen is we're going to hold back all the ones that are not at a particular age and let go ones that aren't. Yeah, exactly, exactly. So we have no analogous cycling in the system. Yeah. OK. And the reason that Helmstetter wanted to sample now age distributions is because they didn't understand how DNA replicated. So I'll tell you what they knew at the time. So Helmstetter's goal was to understand DNA replication. OK, what was known at the time, I sort of moved myself out of board space, but I'll do it here. So what was known at the time was that when these chromosomes, so they knew that the E. coli had a circular chromosome, and when it replicated, there was only a single point of replication. So a single origin of replication. And so it starts, it's like a zipper, if you like. So it starts replicating at this closing point of the zipper, then it unzips like this, and then you have two pieces, and then the cell divides. Is that clear? OK, I said that. I mean, you don't have to tell me, but tell me why it's not clear. OK, then you do have to tell me. Yeah. OK, so this is the DNA molecule that contains all the genetic information. And it looks like a circle, but say imagine a ribbon. Is that OK? A ribbon. And so you've got a circular ribbon, and now you cut it at one point, and then you tear it into two circles. Is that an OK image? Do you have the image that I'm talking about? Yeah, yeah. So what happens here is, so let me first tell you why I contrast this with another model. So here what I'm thinking of is a single tear, and then you pull the whole thing apart. Contrast that with perforating it at, say, 50 different places, and then just pulling it apart. So there's only a single point of replication. And what happens is it some machinery crawls along, so this is indicated by these triangles, crawls along this tear point. So this is called a replication fork. Makes new DNA here. So it pulls it apart. It's a double-stranded molecule. Pulls it apart into single strands, and then stitches on new DNA. So it replicates it. And then as it goes down, this is the old DNA, and this is the new DNA. Does that make sense? So this is one double-strand becomes two double-strands. In principle, they're perfectly replicated. I mean, it's true that occasionally errors in replication occur, and those are what we call mutations. OK, is this OK? So this Y is a blow-up of this triangle area. And so what you have is two forks of replication that are coming down the ring of DNA. And in the end, so you'll go from one ring to two rings, like this. So these are the forks. These are the final replicated chromosomes. Is that sensible? All right, because logically, it's going to start to get jumbled in a second. I mean, not too jumbled, I hope. So this was known. And so far so good. Then Mola postulated that the speed that these replication forks proceed at is constant, irrespective of growth rate. He had no evidence for that, really, but it's a simplest possible assumption. And Mola always went for that. So Mola proposed, let's say, the speed of DNA replication was growth rate independent. And to a good approximation, it is. So let's say that the time it takes to go from initiation of this replication event to separation of the sister chromosomes, so call time it takes to replicate. So you start here. A second later or an instant later, you have this system. Then a little bit later, you have something that looks more like that. I mean, this should be coming out toward you. Just not a very good draw. And then it will be like this. And then finally, you'll have two. So fork keeps coming down. And then they separate. So call this time tau cycle. That's a cell cycle time, if you like. And that's the time it takes not only to terminate this replication process, but to separate the chromosomes and then to divide this out. Is that sensible? So the table's set now. So two questions. One is, if your doubling time is much, much longer than this tau cycle. So suppose this is, I don't know, 60 minutes. But your doubling time is 90 minutes. And that speed is constant. Then what would be one of the predictions? No, no, keep going. Or unless you don't want to. Some cells have more DNA per cell than another and this depends on the new. So now you, OK, I'm not sure. Yeah, yeah, OK. So I'm going to paraphrase what she said, but it's not exactly what you said. But if this thing took, say, 60 minutes and you're doubling every 90 minutes, then you replicated one and a half times per life, then we can't possibly have a balanced state of growth. Because the first time that you grew, you would have 1.5 times your chromosomes. Then again, you would have 1.5 times 1.5 number of chromosomes. Then 1.5 times, 1.5 times, and so on. But you'd have a number greater than one raised to the power n, which is your generation. You would just explode with DNA eventually. So how logically would you have balanced growth if this thing was, say, 60 minutes and you were doubling at 90 minutes? So you would just stop. You'd have a gap of 30 minutes where nothing happens. Then it starts. You have 60 minutes of replication, then you have division. Does that make sense? So if the doubling time tau is greater than tau cycle, there should be a gap in DNA replication. But there should be a period where there's no DNA replication. Does that make sense? So there'd be a period where nothing's happening in the cell for, say, 30 minutes. Otherwise, you would have too much DNA. And it would keep multiplying, multiplying, multiplying. Let me pause. That's important. Does that make sense? All right, two questions then. One is how, yeah, say one more time. You could think of it that way. You could think of it as a maturation time. Something's got to happen until it decides to replicate its chromosome. What that Q is, you know, is debatable, but you're right. You could think of it as a maturation. OK, two questions. One would be, how would you ever see this gap? Because if you had a population measurement, there's so many, I mean, if you're averaging over the whole population, that gap's going to disappear. You've got it only occurring in, say, young cells. Well, fine. But you have the old cells where there is DNA replication, and they wash that out. So the only way that you could see this gap is by somehow isolating cells at different stages of their growth. I mean, there might be another way to do it, but that's what Helmstetter was thinking. Does that make sense? So his motivation is to, in some sense, validate Mola's proposal. But then I think even more importantly, ask what would happen if your doubling time was smaller than this cycle time? If it takes 60 minutes to double this thing and you're growing at 20 minutes, what the devil's going on? This is crazy. All right, so that's what we're going to do today. Does everybody see the problem? Sure. Sure. Because if not complicated, the thing would not be able to divide further. Yeah. If I do that, if the distribution was uniform, then I would have a fraction which would not divide, which would be equivalent to the one set, average finished division, the leftover is taken in my order of the gap. Yeah, that's a good way. So his suggestion is, kill anything that has one of these triangles, and then count how many survived. You could do that. So if you could find something that specifically killed something with a replication triangle, then you'd be done. How about if tau is less than tau cycle, then we're in trouble, and then everybody's going to try. All right, so Helmstetter wanted to validate this picture and then probe the case where tau is less than tau cycle. How did he do it? And so as I said, he wanted to sample narrow distribution from the age distribution. So Helmstetter, and this took 10 years, what I'm going to show you seems like, yeah, OK, in hindsight, obviously. But so do a lot of our committee's proofs. So it's got that same quality. So Helmstetter hit upon a very simple, in retrospect, simple way to sample from the age distribution. So what he did was he took a funnel like this, and he had a filter paper here, and he poured his bacteria through the filter. So he took a test tube full of bacteria, and he dumped it in. Pour bacteria through the filter, and then he flipped it over. And you end up with, so again, the same filter paper. The funnel's going up now, though, like this. And then he ran media through the back end of the filter. So now this is a poor drawing here. Now fresh media starts dumping through like this. And as luck would have it, some of the bacteria would stick to the filter paper. So you'd end up with some, let's see, this guy's halfway done. This one just had a baby. So you had some cells stick to the filter. That's these guys. These are called the mother cells. And as they grow, so their heads are stuck to the filter, as they grow, their daughters drop off their feet. And so as they divide, their daughters or babies washed away. But the babies who fall off all have the same age. They're freshly newborn. Does that make sense? And this came from a dream that he had of chickens on the roof dropping eggs on his head. It's brilliant. And so this came to be called the baby machine. It's super cheap. It's super easy. And you'll see in a second that it cracks this question wide open in a way that was impossible beforehand. Okay, but let me pause. Someone had a question? Yeah. Yeah, yeah, yeah. Yeah. Are they stick to the chipper and also stick to the filter? Yeah, you'll see that. So her suggestion is that this is highly idealized. Not all of them are going to be stuck at the poles. And that's absolutely true. Some of them will be stuck sideways. Some of them may eventually fall off. That's quite rare. But the sideways one, you'll see that quite a few of them do stick sideways so that their progeny remains fixed to the funnel. But you'll see where that comes in. Well, actually, let me tell you what this looks like and then imagine what's going to happen. Is the experiment okay? Do you guys see what's happening? And so what happens is, I mean, mathematically what happens or graph what happens. Is it with the mothers? So when they get stuck to the filter, they have this, it's just a billion cells that follow this distribution. So this is in some sense the number distribution of ages in the cells that get stuck to the filter paper. And so then as time goes on, so here's tau. Here's two tau. Here's three tau. This is the babies. Baby cells. And I'm going to call this flow the effluent. So it's sort of the waste media, if you like. So what's happening? These guys fall off first. So let's call this T1. Then later on, the babies from these cells fall off. Does that make sense? So you've got them all stuck. They're very big and about to have a baby drop their baby right away. The ones that are newborn, they have to grow and then they drop their baby. And so what's that distribution going to look like? So again, remember that this was a probability distribution. Now I'm multiplying it by the number of mothers that get stuck to my filter. So now it's a number distribution. What's a number distribution going to look like here? It's probably easiest if we think of zero to tau first, like this. One possibility is it looks like this. What do you think? One more time, the mother cells. No, no, no, exactly right. So you also have to assume that the sticking probability is uniform across the population. And to a good approximation it is. So there's no bias. This guy, yeah? And so then what will you get? Who falls off first is maybe the best question. It's a little image. So it's going to look like this. So where this is, if I say, you know, relative concentration, say, where I don't have to worry about normalization, this would be two. This would be one. And then boom, boom, boom, boom. And then this would go up. And this guy would go up. Because these guys are the T1 cells. And these guys are the T2 cells. Does that make sense? So in the babies, it's like time is reversed. That's small step, but sort of, you know, disorienting step number one. Okay, so in the babies, age is reversed. I don't know if that's the best way to say it, but hopefully you see what I'm saying. The ones to fall off first are coming from the oldest cells stuck to the filter paper. Yeah. Oh, yeah. So this is after there is a transient. You're right. So this is say, you know, wait for the transient, wait for the first division, then start. You're right. I mean, it'll go like this. Is that okay? So ignore the transient. Does that make sense? What I want to orient you to is this inversion. So do you mean why is it decreasing here? Oh, oh, oh, should go. Yeah. What do you think? So two things here. One is that it's flipped in time. Is that okay? Now, why is it not an escalator? So it's exactly. So he's exactly where you guys. So this is probably the image to keep in mind. Once this event happens, that age resets itself basically. It grows, dumps its baby, but the baby has left the system, left the filter paper. So it's as it was a generation ago. Ideally, but your previous question is going to come back. Okay. So is everybody. So first of all, the time is okay, I think. But now how about the drops? Drop. Drop. Is that okay? Yeah. Exactly. Exactly. That's the problem. If they were synchronized, we wouldn't need to go through all this because we would have, we would have, we would have zero peak, zero peak, zero peak. This dropping is because, it's because once the baby is born, she's washed away and only one of the mother's remains. And so it's, it's as though you reset again. So this is, this point here is where the newborn cells have their babies and they're them because there were more newborn cells to begin with stuck to the filter. But now suddenly it's a periodic boundary condition. You end up now looking at the, the oldest cells who are now ready again to, to have babies again. So you keep moving through this distribution backward in time with a periodicity. Does that make sense? And the reason it's not cumulative is because the babies don't stick to the filter. If the baby's stuck to the filter, wow, this, this wouldn't make sense. It would just be zero. And you would end up with that and that. Yeah? Okay. Yeah, yeah, yeah. Let's look. Yeah. You would, right? But what turns out is that you have more of what she suggested, which is that the baby stick. And so here's the picture that I have, or this is the data. So ignore the kind of transients. Who was worried about transients? So ignore these transients. But this periodicity comes from the cell division cycles. This slow upward creep comes from babies getting stuck to the filter. And so there are, there are, you know, many non-idealized factors here. But the overall sort of tup, tup, tup is what they're after. Yeah. So, so this, this thing is kind of going up like this. What's, what's also brilliant about this experiment is that it doesn't matter that these things are going up. That there's some slowly creeping offset. It doesn't matter because what he's going to be measuring is delta changes in a secondary quantity that I'll talk about in a second. But I just want, I just want conceptually people to see that this, this oscillation comes from that babies getting born. The slow creep up comes from what she was suggesting, which is that babies gets, you know, don't, in an ideal world you would have just a flat baseline, but you have inevitable creep. Yeah, exactly. So, so as she says, this is not particularly because of this creep. This is not a sustainable, I mean, this is his first run at it. People got decidedly better at it and developed filters that were decidedly less prone to this. But you can see that you probably can't go too many more generations without this thing just looking like movable. And you lose a signal in the noise, right? And then you also have these problems as she suggested. If the density on the filter becomes too high, then it's not, you can't guarantee that they're growing exponentially in some balanced state. If that makes sense. And so at best you can maybe get, especially in his first run at this experiment, you can maybe get three or four or five generations reliably. But it will turn out that that's all that he needed. Okay. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Well, he's going to want it. So there's, there's three things here. One is that this is a finite amount of time. Okay. Fine. But then you want to sample the population that washes out to be high enough that you can measure reliably. So you want something of the order of say millions or tens of millions of cells. So you have to either really ramp up the amount of cells that you stick to your filter. But then what if they're not in balanced growth? Or you ramp up your window of time. And so there's optimization that you need to fiddle with, right? And then this question of, of growth rate is something that he wants to toggle independently. So at each growth rate, you would need to, you know, fiddle with these things to make sure that you're not incurring any sort of problematic artifacts. But in the end, what he's going to do is run this experiment. In fact, these are all different growth rates. And his sample period, I think it's for about a minute. So he, you know, holds us big and open for a minute and samples us. All right. So this, this is not yet the experiment. I mean, this is the setup. This is the baby machine. This is the narrow sort of ticking out of the population. But we haven't yet said why this has anything to do with DNA replication. And as it stands, it does not. So, but we'll get to that in one moment. All right. But I want this to be clear because otherwise it just starts to get foggy and foggy and then it's just incomprehensible. But is this okay? And I promise you, if it's not clear right now, it'll just take two minutes to clear up. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. So here is more or less a transient as things. So you've got a big puddle of cells at the beginning. You dump them and they wash out and then you have to let the system equilibrate a bit. And so it sort of takes a little bit of bouncing around. Is that, I don't know if I answered. Yeah. If my faith is a prediction as I go into the patients right. Yeah. And that's because the babies are sticking to the filter. Which is, which is, you know, you want that not to be there. The other thing too is that these are not sharp, I mean they should be vertical, but they have some, what would you call it, slope, non-infinite slope if you like, right? And that's because the age distribution in practice is not delta distributed, and so you have sort of a curve here, all right. But again, these are all small points that mercifully don't impact the experiment that we'll talk about in a moment. But again, let me pause, anyone want to clarify this? Times flipped, yeah, yeah, yeah. So this, think of this as a relative concentration. So this might be six billion, and this would be three billion. And it would go, there would be, there are half as many about to have babies as there are who were just born. And that's because when they're born they make two here. So these guys are falling off of this part. And there are, there are half as many, so here, there are twice as many here as there are here. Does that make sense? Okay, all right, I should have labeled both axes. Any other questions? Okay, let's get to the weird part. So the way that Helmstetter wants to look at DNA synthesis is the following. So he will, he has his cells growing in a flask, and then he's going to dump them into this filter. But before he does that, so to, I should turn this off if it's not relevant. To measure DNA synthesis rate, he does something that's called pulse labeling. So he grows his cells for one minute in radioactive thymidine. So, I'll write it up. And this is one of the DNA bases. So it only appears in DNA. I mean, there's free thymidine, but not much. It doesn't appear in RNA, it doesn't appear in proteins. This is a chemical that's specific to DNA. And you can get it, in the world it's just regular. It's made up of carbon-13, but he's going to get especially made carbon-14 thymidine. And so then he, for one minute, lets his cells grow. And then he flips them and pours them through the filter paper. Okay? Then flips or pours them through the filter. And then he measures the radioactivity in the cells that come out. So the new media that he pours through has no radioactivity. The media that he grew them in before had no radioactivity. And so what he's trying to measure is the number of forks, basically. Because the amount of radioactivity that a cell takes on in this one minute is proportional to the number of forks, replication forks that it has going on. Okay, so his idea is the following, and then let's talk about it. So his idea is the level of radioactivity in a cell is proportional to the number of forks, the number replication forks. Okay, so you have them exposed to this radioactivity for one minute. If it has two forks, then it takes in twice as well, two is okay. So if it has two forks, it takes in a certain amount of radioactivity. If it happened to have four forks, for example, it would take in twice as much radioactivity, if that makes sense. Or if it had no forks, it would take in no radioactivity. And then suddenly when it had two forks, it would take twice as much radioactivity, if that makes sense. So everybody see what I'm saying? So by reading the radioactivity in the baby cells, then he should get some sense for the number of forks that were going on at that age in the parents. It's like three levels of inference, but hopefully they're okay. Oh, you just put it into the media. So you grow them in regular media. Probably there would have been, I wonder if he supplied the thymidine. He probably does. So what he would do is grow them cells that can't make their own thymidine. He would supply it in a medium non-radioactive. So they're bringing it in and incorporating it. And then he would add radioactive thymidine in huge excess, like say 500 times more than was in the media to begin with. Then you're guaranteed that the thymidine that you're taking in is radioactive. You've like less than 1% of a chance to take in a non-radioactive thymidine. Does that make sense? You have to make sure they can't produce their own thymidine. You have to make sure they can't produce their own thymidine, otherwise you have to label all the carbon sources. Does that make sense? Yeah. Is it lethal? Oh, I see. So this was, although less so now because of safety regulations all over the place, but it still remains a fairly standard procedure in biology, is if you want to label something, and now we do with fluorescent proteins primarily, but labeling with radioactivity is a well-established practice. It turns out that radioactivity is usually non-hazardous to us and to the bacterium. Is that what you mean? Is that what you're worried about? Or that the chemicals are distinct enough that the cell will treat them differently? Yeah, yeah, okay. So they don't seem to incur mutations. They're not high enough energy radiation to worry too much about that. Any other questions? Okay, so his idea is this. Suppose you have the mothers. So now we're gonna talk about the mothers, and then in a moment we're gonna talk about their daughters. So here are the mother cells, here are their ages. Suppose something like this happens. So this is now radioactive, radioactivity per cell. Suppose something like this happens. What would you suppose was going on? So this is now relative radioactivity. So it was one, and it jumps to two. What would be your interpretation? It could be, yeah, okay, even easier would be the gap one. So suppose the gap goes like this. Now it's gonna be in absolute units. But how would you interpret that? What does a change represent? Division happens at the end. What do you mean? Division happens at the end. So division happens at the end here. So this age at which you see a jump corresponds to, so a jump, let me write it out and let's talk about it. A jump in the relative radioactivity per cell, per cell corresponds to the initiation of DNA replication. All of a sudden on the scene appears two replication forks that can pull in radioactivity that weren't there before. And this line that I've drawn then is what, I mean, I think could be reasonably denoted the age of initiation or initiation age. Now let's say age of initiation. And so for cells that are growing much, much longer than the cycle time that it takes to replicate the DNA, that age of initiation would make up the gap. And it turns out that it's actually like this. It's a gap at the beginning of the cell, cells lifetime. And then DNA starts to replicate and then terminates its cell division. Does everybody see the logic? Yeah. No, OK, so I have in mind the case where the cell is not replicating its DNA. So this is a cell doubling, say, every 100 minutes. And yeah, but it doesn't suck in this radioactive thymidine if it's not replicating DNA. That's the key. That's the brilliant part of this. It's only going to take in this radioactivity if it's replicating DNA. It's a logically compelling argument. I mean, it has to be clear otherwise then it's not compelling. But is it clear? Exactly. So this would be the case if this replication time was much, much longer than the time it takes to replicate DNA. Yes, yes, exactly, exactly, exactly. Yep, exactly. OK, all right. And so what? Oh, that's not what I wanted to do, sorry. This is what I wanted to do. OK, so I'm going to tell you about the experiment he did in 1968. In 1967, he looked at slow growing cells, saw this gap, and he was very pleased, very excited. Because the benefit of this experimental setup, in addition to being cheap and super easy, is that you don't touch the cells after they've been labeled. You label them when they're growing exponentially in a flask. So you're no more sort of prone to people shouting at your experiments because they're artifacts than anybody else who is doing radioactive labeling. And everybody's doing it, so nobody's going to get mad about that part. Then you dump it through his filter paper. You haven't touched it. It's still growing exponentially in balanced growth. It's a minimal perturbation. It's no surprise that Helmsfeder spent a lot of time in Mola's lab. So they're very sympathetic in their approach to these systems. And Helmsfeder was trying to find a way to do this without perturbing the cell, without your observation disturbing the information that you get out of it. So in 1967, I want you to get the data because it might be tricky. It's better if I show you the new data from 1968. So this is now, Helmsfeder is growing cells that are much more rapidly growing. So they have doubling times of, say, 30 minutes, 40 minutes. And he's joined by Cooper. And together they look at this data. And what he sees is, so this is radioactivity in the mother. And so in the baby cell, so this is now radioactivity. And I'm going to put this on a log base 2 scale. Log base 2 of the radioactivity per baby cell in the effluent. And it's going to look like this. So here is 2. Here is 1. Here is 0.5. Here is now 0.25. So these are equally spaced because I'm on a log base 2. And I want to show you what he sees. So he'll see what's going to happen here. Zoop, zoop, zoop. And then he'll see this thing go up. I'll get out of the way in one second. I just want to do that. He saw this. And so the interpretation is that you have something that goes like this in the mother. So we won't yet talk about why this thing looks so weird. We will, however, talk about what he measured. So then he measured this. So he said the first time that you see a rise in the DNA replication rate corresponds to the triggering or initiation of a fork of replication. Does that make sense? I mean, not the bottom plot. So he used the bottom plot to infer the upper plot. And then he measured this time this age. Yes. How do you mean? Wait, sorry. Here? No, this is the age. So there might be some transient here. But you set 0 to be the point where you had the first division. So absolute time now falls out of the equation. You're talking about here? Yeah. Yeah? I think we're doing the same thing. Yeah. I'm looking at the first one. Yeah, these are the same points. Oh, yeah. But you're only, yeah, so the mothers are unsynchronized. So, OK, so you have this situation for the number of mothers. Is that all right? Yeah? This might solidify the discussion. Is that OK? Yeah? And then you throw radioactivity on them. And then you allow time to advance by one minute. And so everybody that's at this age plus delta A takes in their amount of radioactivity. Everyone that's at this age for one minute takes in radioactivity. And so it's an unbiased sample of the population of what the person at that age or the mother at that age is doing in terms of their DNA replication. Yeah, OK, yeah, yeah. So this minute is enough for you to get hundreds of bases of DNA. And so you lose any, that's important too. The thymidine is not biased either. Any other questions? Is that OK for you? It's OK? So it's, I mean, there are like five different things happening here. But the thing is that they, so for the one minute that he lets them be exposed to the radioactivity, they have some consumption rate. And so you integrate that rate along that one minute time. And that tells you how much thymidine comes in. So there's an integral going on. And that integral then integrates across this amount of space. And that tells you how much thymidine comes in. But then you put on top of it this, which is telling you, so these guys consume at some low rate. These guys consume at some very high rate. And these at some moderate rate. And so if you integrate a small piece of that, you should get a little less radioactivity than if you integrate over a small piece of this. That's the idea. Yeah, yeah, yeah, yeah, yeah, right? Exactly, exactly. Let's go, can you just hold it in your mind for one second? And then let me show you what the plot of this looks like. OK, and then, so let me show you the plot. And then we'll break. And you can think about what the plot means. And so now if you look at the doubling time, so this is doubling time. And this is the relative age. So now this is going to be the age of initiation divided by the doubling time. So you count this, it's like five minutes first outgrowing at 30 minutes or something like this. And so this will be between 0 and 1. And this is going to have real units. This is something that you're using your watch to count. And so I'm going to start. So these E. coli, you can't really grow them any faster than say 20 minutes. So 20 minutes, let's say 30, 40, 50, 60, 70. I'll give you one more, 80. All right. And so for very slow-growing cells, this is what he's observed in 1967, this age of initiation goes like that. It increases. And it increases for the reasons that was suggested earlier. There's a gap. And then it starts replicating. But then there's suddenly a discontinuity. And you have it jumping up to 1. And then falling down again. And then jumping up to 1 and falling down again. And if I've timed this correctly, there we go. So my plot is idealized. But this is the data. And he's left off the data from 1967. But I put it in here because I want to be able to possibly solve the puzzle. So does everybody see what I'm saying? He's got these weird shapes, which will come back to in a second. Like after the break. But more importantly, he's got these discontinuities in this age of initiation. And they look exactly like this. So boom, boom, boom. Does that make sense? So he doesn't see a spike here at all, really. But then I'd say 58 minutes. He sees a spike just before division. And then that age sort of creeps closer and closer. And then a spike just before division at about for 28 minute growing sense. All right, does the data make sense? I mean, not the interpretation, but does the actual plot itself, do the axes make sense to what he's measuring? And again, it doesn't really matter that the data itself was creeping up or anything like that because he's measuring jumps in radioactivity. And so that you can get pretty accurately, irrespective of some baseline shift, which is one of those great things. All right, let me pause. Yeah? Oh, get the plot. So what he's doing is he runs this type of experiment at different growth rates. He knows where the cells are dividing because he knows how the number count is going. And then he measures this gap. He says, all right, going backward in time, he actually plotted them flipped around, which is a double mix up. He measured this time, which is an absolute unit. So it's, say, 15 minutes. So he writes that down. Then he does it at a different growth rate. He gets 10 minutes. He writes that down. And then he plots the age of initiation divided by the growth rate. And he gets some number between 0 and 1. And he does that for all these different growth rates. So this he can change by changing the nutrient that the cells are growing in. This he measures from this radioactivity jump. Is that OK? Just where the data is coming from, not necessarily why it's jumping around like crazy. But is the data, where the data is coming from, OK? Pardon me? OK, no, think about it, though. You don't worry. So this is a real puzzle. All right, any questions about what the data means? All right, we'll simultaneously answer four questions right after the break. So your original question, why does a DNA increase with growth rate, has been just lurking in the background for days? So we'll come to that. And your question of why would it ever overshoot is going to happen. We'll talk about that in like five minutes too. All right, a new pause. Oh, and what we've never talked about is why does it take one hour, why is one hour doubling special for that mass per cell plot? That's also going to be cleared up. All right, any questions? All right, OK, I'll see you in like five minutes, 10 minutes. It's how they got this data or how they rationalize this data. But I think it's easier for us in retrospect to figure this out. So what we now know is that to go from here to here to here so the fully replicated DNA takes about 40 minutes. Now to separate. Oh, gosh. Sorry. OK, apologies to the camera guys. They go from, oh heavens. Double apologies. So all right. OK, I think. So to go from initiation of DNA replication to fully replicated chromosome, Molly was right. I mean, it's mostly growth rate independent. And it takes about 40 minutes. And then the cell has to do, I mean, it's physically there's nothing else it can do. It needs to separate that DNA into its daughters before they divide. And so to go from, so these are now just completed, replicated chromosomes to separated and divided, that takes about 20 minutes. OK, so we have these two processes. And so Helmsted and Cooper called these two different names. So they called this the C time and the D time, which will be, it's just a nice shorthand. But the C plus D is going to be the cycle time. Does everybody understand what I've drawn here in terms of cartoons? No matter what you do, these forks will take 40 minutes to get from the beginning to the end. No matter what you do, it's going to take 20 minutes for these DNA strands to separate into their respective daughters before cell division. All right, so to move from initiation of replication to termination of replication takes 40 minutes. To go from termination to cell division takes 20 minutes. And there's nothing you can do about it. Now here's the question, why can a cell double every 20 minutes? It seems impossible. So what's the resolution? Exactly. So you parallelize this. You initiate multiple forks of replication. So how do we divide? Do they divide faster, 60 minutes? And the answer is multiple forks. And so we saw this. I mean, we didn't make a big deal about it when we were talking about protein synthesis. But ribosomes, which are driving protein synthesis, work for the most part at full blast as fast as they can. So then in order to make protein faster, the cell can't turn the rate up. It just adds more ribosomes. It parallelizes the process. It makes a production pipeline. The same thing goes here. We can't make these forks move any faster. All right, add more forks. It's incredible. I mean, it's a really clever engineering strategy. And so what you end up with then is something that looks like this. You have one set of forks here. And there's an origin of replication like that. And then you would have another set of forks here and another set of forks here. Oops, what have I done? What am I doing? Good heavens. Oh, yeah, no, that's good. Forks here, forks here. That's horrible. Let me drop a nice picture. OK, so here's a fork. Here's a fork. Here's an origin. Here's an origin. And then you initiate a second origin. Here's a fork. Here's a fork. Here's a fork. Here's a fork. And there's another replication. So here we have simultaneously 1 plus 2 rounds of DNA replication. And so when you have something like this, you'll have one round here for 1, 2, 3. So this would be the synthesis rate. We'll go from 1. Then you initiate the second rate. You'll get 1, 2, 3, 3 times more synthesis rate. And then you'll drop down to 2. So this is with 2 forks. This is with 2 plus 2 to the 2 forks. And now this is just 2 to the 2 forks, if that makes sense. So now you've got 2 forks coming down at the beginning. And then halfway through, well, whatever, a third of the way through the generation, you initiate these new replication sites. So you have these old forks plus these new forks. A blink. And then you keep going. And this fork, these two forks meet at the bottom and terminate. A blink. But you don't fall back to your old rate because you still have these two simultaneous forks proceeding. And so what Helm said it was measuring was this first age. And so each time we get a discontinuity, that's initiation of a new or that's pushing initiation of DNA replication back another generation. So I'm going to unpack this a little bit more and then we'll break lunch. But what's going on here is that the bacteria themselves are self-initiating. So I wait, I wait, I initiate replication, and then I divide. And it's all me. But here, your mother is initiating replication for you or better not anthropomorphize it. The mother is initiating DNA replication for their daughter. And so the daughter is born with a half replicated chromosome. And that's how they're able to double much faster. And here, the grandmother is initiating the chromosome. The mother keeps growing the chromosome and impasses it onto the daughter almost fully replicated. It's extraordinary. Does that make sense? I mean, it doesn't need to make sense, but just in general. And then we'll look at it quantitatively and we'll sketch it quantitatively today, but then we'll go into it in more detail tomorrow. But now, so that's why the DNA is increasing. It's not that it's a different species. It's that you're carrying redundant information for your daughter later on. But this leads then to a point that notice that the DNA that's close to the origin is effectively amplified by a replication. And the cell can take advantage of that. We'll talk more about that maybe tomorrow. But does everybody understand this parallelization? It's extraordinary. I tell you there's a speed limit? No, there's not. You add more cars to the road, basically. Yeah, yeah, exactly. And so if you look back, so I think it's probably gonna be easiest to sketch it the way Helmstetter did, which is graphically. That's the way that I gravitate to, but then that sometimes doesn't work. And then we'll do it analytically with pencil and paper. But you're exactly right. So as you go past these discontinuities, you're moving from self-initiation, mother initiates, grandmother initiates. And if you could grow faster, your great-grandmother would initiate and so on. And you'd have these hugely branched DNA loops. Any other questions? And so what we have then, I mean, this isn't how Helmstetter described it, although it is graphically how he derived his rules, is a tiling of a continuum of division times. So these are dividing whatever they might be dividing, say, for every 45 minutes. And that's what I do by fixing the chemical composition of their test tubes. And I can change that any way I like. But lurking underneath that is a discrete tiling of that continuum in chunks of 40 and 20 minutes. Tom, tom, tom, tom, tom, tom, tom. And the cell, of course, has to figure out how to do that and it does it, but that's regulation. What we're talking about here is phenomenology. Given that the regulation is there, what can we predict, for example, about the age of initiation? Okay, and so Helmstetter went the other way. He looked at this data and inferred this. Well, he and Cooper, which is an extraordinary act of mental agility, I think. But I'll show you how he did it tomorrow, I guess. I'll show you tomorrow how he did it. And if you feel like it, you can just read the end of this lecture. And as I say, he just literally drew tiles. So one tile that was the division time. All right, I'll sketch it. It'll just take one minute, then we'll break for lunch. So Helmstetter's is tile the generations with strips of 40 minutes or C minutes and D minutes. And so, for example, he would have, let me see what his picture would look like. And again, I'll just start this. So he used squiggly line for tau equals, say, 35 minutes. And this works much better if you've got a piece of graph paper to do this on. So I'm gonna freehand it, and it's not gonna be the scale, but the next line would be the 40 minutes. Oh, it's not bad, but. And then a dashed line that was half as long again, which is D equals 20. And then he moved this over and repeated the tiling. So he would have this and then this and then this. And then again, so, and this is again, this will be the last thing I draw, and then we'll break for lunch. And did I do that okay? Yeah, and you would keep going until, depending on how fast these cells are growing. Does everybody see what I'm doing? I've got a strip, and then I just keep displacing it. Ideally, of course, you would have these squiggly lines as you're in the background, and then you would lay transparent pieces of C and D on top of them, and then just look at the darkness or something of the transparency. But here he's separating them. And then if you look from here to here, you have a complete record of what's going on inside the cell during one division period. And so what you have is DNA replication up to here. So now if you look at the forks herself, you would have, say, one fork, or one pair of forks. Then here you would get, so this is now two forks, let's say. This would jump, this would be two plus two squared forks, because each one of these initiates a new round. Oh, this one terminates, but these guys are still around. So you get two, two forks. Till the end here. What did I do? What have I done? Sorry, this ending should be here. There we go. So from this point to this point is one cell division. These solid lines tell you the history of the DNA replication, two forks. Then each of these forks initiates a fork. This one terminates, but leaves its progeny forks. And so in this way he was able to rationalize those very strange DNA replication graphs. I mean this is graphical, and to try and extract an analytic expression for these ages of initiation, doesn't look like it's gonna be easy, but it will be pretty straightforward. But I think it's best if we let it stew and then we'll talk about it tomorrow. That's okay. But let me pause though, just if there are any clarification questions, and then we can really resolve this tomorrow. Any questions? Yeah. Yeah. And so her question is, what about the media? How does the growth medium affect this? And it seems to not affect it at all for a given growth rate. So irrespective of the composition of your growth medium, if you're doubling it one, doubling every 35 minutes, it will look exactly the same, no matter what the recipe is. And so that's one of the great findings of Mola, and it continues here. So, but we'll talk about that tomorrow. Any other questions? Oh no, there's randomness. Yeah, yeah, yeah. So the question is, is this true at the single cell level? Of course, expected distribution at the single cell level for all of these parameters. All right, and that's stuff that people are measuring these days, but are impossible at this time. Any other questions? All right, great. So let's all have lunch and I'll see you guys tomorrow.