 Okay, so everybody had access so that's not an issue. Is that true? Is that okay? Okay So what I'll do just in case is I'll make it so that it's linkable from my web page at at the University. So if you Google search Matt Scott Waterloo and then looking for the teaching page It will be accessible from there. Okay, and the in the password is a node M-O-N-O-D all lowercase Okay, if you got the link from from America that's all taken care of it just goes right to the page All right, so if you give me 10 minutes after the lecture by 430, they'll be accessible. Okay What else can I tell you I Think that's it. Yeah So let me bring you back to what we were doing at the beginning or the end of last lecture and then maybe we you know Let me know if anything's come up since then so we ended looking at this review by Minot with these different phases of growth So you come in in the morning you put your bacteria in your growth medium And you let them grow over the course of the day you see that nothing happens for a while Then suddenly they start growing exponentially and then that tapers off and they stop growing and then they all start dying Right and this for a long time was the main focus of Bacterial physiology if you want to call it that For say 50 years and people notice certain things so it's very much like the study of Brownian motion So for you know for about a hundred years people made qualitative Insights here and there but but nobody had an overall picture until 1905 obviously and So people notice for example that cells here were smaller didn't seem to grow as well Cells here were smaller didn't seem to be growing as well. Whatever that might mean here They seem to be big and growing well, but there was nothing to tie everything together. Okay, and so that's the status in 1949 We still don't know anything that I talked about earlier, which is this circular chromosome Robizomes and all of that so we're gonna talk about today or for this lecture is where that view came from We have it you and I but let's look at the experiments that led to it. Okay. Yeah Yeah, so here this end is any cell that will give a colony when I played it out on that agar So here it might not be growing But if I put it on to the agar plate and I wait long enough it will give rise to a column So the the sort of the catch-all that people use is viable cells So they may not be growing here, but they they're viable. They could grow Here this is bonafide death their numbers are decreasing and so you plate them out They don't make any colonies. They're they're they are dying Does that make sense where this end is going down? So you might have a million cells here and then you wait a half an hour And you try to plate it out again, and you get ten times less colonies coming up And it's perfect. So this looks like a lifetime, right? You're going from birth to maybe old age to death Right, and that's how people were viewing it as sort of an intrinsic property of the bacterium this life cycle But but there's something magical that's going to happen in 1957 and we'll come to that in just a moment. Okay Any other questions I Yeah, yeah, okay, so he's saying well what I'm gonna paraphrase it's not exactly what you think But I want to twist it a little bit. So what he's saying is this is I don't understand why they go extinct Can't you just feed them or nutrients or or dilute them? You can right and so the thing that that was missing here was something that's called balanced growth You see and it's a very small shift, but it made it all the difference. It suddenly People went from not understanding anything to having some framework within the understanding everything Okay, and so what's missing from this picture and it comes back to your question is So what is missing? from this picture So I'll tell you what's not missing. What's not missing is that people are thinking of bacteria as just a test tube representation of humans and we do that all the time Everything everything comes first to us like you know for I'm thinking for example of our views of the universe The earth is at the center. Why wouldn't it be and then suddenly you break that and everything opens up and so here we're thinking of bacteria as a Not spatially localized, but still it develops away human develops You break that suddenly everything opens up and so what's missing from this is something is called balanced growth and Balanced growth mathematically is not going to shake the world But it's a conceptual shift that as I say opened up a decade-long golden age for bacterial physiology And so this is an idea that Campbell came up with in 1957 And it's the it's what I'm going to call a standard reference reference state. Sorry. So it's a Steady state of growth a reference state All the constituents of the cell double at the same rate. So mathematically you might think of this as steady state exponential growth So what Campbell says is focus your attention here That's the most important spot. All of these are experimental artifacts Exponential growth is the real key to what's going on here And you can see I'm why I mean it's not obvious at this point But focusing in on exponential growth imposes huge constraints on what can be going on inside the cells And so we write it out as the as a simple differential equation So we say dn dt is equal to some lambda and where this is our exponential growth rate And you might have seen this even at high school when we say, okay We saw that it's an exponential things like that, but there's something really deep going on here if the cells are doubling once every hour Then what do you know about the DNA content? It doubles every hour the RNA content doubles every hour the protein content doubles every hour like clockwork the whole thing this whole Sack of chemistry Arranges itself so that its contents double it precisely every hour I mean there's some fiddle room maybe five percent or something like that But the point is there's this huge amount of coordination that's going on to give us this very simple empirical relationship Which is exponential growth and as I showed you at the end of last lecture This is a very good description of how blessing these cells are growing in this in this Period of their of their phase and so with this notion of balanced growth Campbell took this bacterial growth phase these inevitable lag Exponential stationary and he broke it apart and he said just look here and Dilute and you can keep these cells going forever. They never grow old. They have no lifetime They exist perpetually and you can put them into this balanced state where you know that they are going to double once every hour Everything inside of them is going to balance double once every hour Okay, and as I said at the end of last lecture this growth rate once it's been achieved And once you've you've attained this balanced state is incredibly reproducible So you give me the bacterium that you were using two weeks ago. I grow it in precisely the same Media, you know, whatever the chemical recipe might be. I'm going to get exactly the same growth rate as you So this is a lot like in in thermodynamics where we have 25 degrees centigrade one atmosphere of pressure and so on Do your experiments there and then we'll compare what we get you need that Otherwise, there's no I mean quantitative science can't be done without a standard reference state and that that became apparent in 1957 Okay, so coming back to your question. They're they're immortal if you feed them enough. They'll live forever Not the individual but the progeny so they divide so you lose this notion of individuality But the the bacterium and its DNA will last forever if you keep feeding it It's okay. All right Any questions it's a huge perceptual shift, but for us, I mean it just means you're looking at this line rather than these five lines with four lines Yeah, right. I think I so the question is what's he what how long can a bacterium live? And this these okay, these are deep waters and so I'm just going to scratch the surface but if you think of these bacteria they divide and they divide and they divide and they divide and so If we talk about there's no real notion of aging of these bacteria You can inherit maybe your your mother's pole and so you could think that as the generations go you'll have some Bacteria that have one new half and then one old half. Is that sort of we think? But as far as we can tell there's no change in its growth rate after hundreds of generations. So what we'll talk about Toward the end of this week is some of the the new technological Advances that have allowed people to ask and answer questions that were not available in the 1950s and 1960s one of these is the ability to Isolate a single cell a single mother cell and watch it for hundreds and hundreds of generations and look at its growth rate And you see you see no change It's incredible. So so they really have no there's no notion of age. They live forever As far as we can tell Any other questions? Is it they're really very different from humans? We don't want exponential growth our body fights like crazy to keep things from growing exponentially Except when we're developing so embryonic development is a whole different issue But then if you get exponential growth in your lifetime, it's a cancerous tumor and it's terrible. I mean, it's you just can't stop it All right So with this standard reference state this balanced growth Suddenly as I say a golden age opened up. So from 1958 to 1968, which is what we'll talk about today and the next couple of lectures Was really I everything changed so so with this Standard reference state we had a golden age from 1958 to about 1968 And so what I'll do is is go chronologically through the discoveries of that period because I want to take you through the the the first paper is Remarkable and that's going to be have sort of repercussions that are not obvious but the second one that we look at takes Takes a lot of quantitative thinking to get the the conclusions that they get Okay, and so we'll come to that probably in about an hour or so. Let me start with the first paper from 1958 Okay, so this is Shaktar Mola Kill guard 1958 you can see that it didn't take long For people to exploit this idea so the main guy here so Shaktar and Kill guard are postdocs in Mola's lab in Copenhagen and Mola is one of the great great scientists, but definitely one of the great bacterial physiologists and he so these are This is worked on in Mola's lab in Copenhagen and his philosophy was look, but don't touch so when you do experiments and this was this was He took it very seriously So if you're going to study the growth of bacteria He designed all of his experiments in such a way that there was a minimum perturbation to the to the bacterium itself Which you know principle sounds easy to do, but it's incredibly difficult To try and keep these guys growing happily and take measurements and not disturb them All right, particularly if they're growing very quickly. So his his motto if you like or his was look, but don't touch and So he he perturbed these systems minimally which meant that he for the first time in his lab had data of Unprecedented quality nobody else was doing experiments like they were doing experiments and that meant in turn that they could Quantitatively think about these these systems like no one had done before Okay, so what I want to talk about is this first paper from 1958. It's the first of a two-part Series published back-to-back the first one is steady state So these these cells are in balanced exponential growth And all they do is look at the chemistry. They say how much DNA per cell is there? How much mass per cell is there? How much RNA per cell is there? Okay, and so the first this is the first of two fundamental papers published Back-to-back and I'm going to when we talk about them I'm going to talk about the first one that I'm going to stick in a paper from 1960 and then talk about the second Okay, because this one the first one is a steady state or balanced growth and the second one is about growth transitions All right, so we'll talk about the steady state first Okay, and then and then we'll talk about another paper and then we'll go to transitions and transitions are where you let them Gain bar or adapt to balanced exponential growth and then you shift them to a different growth medium And you have to do that shifting so as to minimally perturb the cells That was a challenge. All right, so let me tell you about this first thing. So this is before E. Coli had been fully Pardon me Had been decided upon as a model organism, and so they're working with Salmonella Which is very closely related to E. Coli and so if we repeat these experiments in E. Coli will get essentially the same thing But that's a small caveat Okay, the idea was they had 20 different growth media and so they'd have so you know this this sugar and this nitrogen source and mixing and matching all kinds of different things and Then they grew Salmonella and balanced growth so they grow and balanced growth And I tell you how seriously they take this they they put the cells into balanced exponential growth for at least 10 generations Before they take any measurements. So these are in in bonafide steady state. There are no transients left And then they measure the growth rate and they measure the growth rate by plating these out and counting cells And they do that 10 times per doubling to make sure that they've got enough statistics to reliably tell you what the growth rate is Insane particularly because some of these cells are doubling about once every 20 minutes And so every two minutes they're plating out these cells and counting them And so what they count so they'll they look at Mass per cell RNA per cell DNA per cell at these different growth rates. All right, and so What I want you to imagine is two two different growth media I'll denote them by symbols. So let's use a triangle and a square So these are meant to be flasks, but it was a better draw. These are two beakers in your in your laboratory And this one has some poor carbon source, but a rich nitrogen source for example This is poor carbon rich Nitrogen and this guy's vice versa. So this guy's rich nitrogen or rich carbon say and poor Nitrogen and by that I mean it takes a lot of of Different proteins to chew up this carbon source, but not much work to to metabolize this nitrogen source and vice versa So if you want something specific, this would be say ammonium the ion and this would be say succinate or something This guy would be glucose and this would be some amino acid that the cell has to break down before it can peel the nitrogen group off But you engineered in such a way that in either flask the cells double once every hour once Okay, does that make sense? So chemically the flasks are very different Microscopically the bacteria are are turning on and turning off Vastly different repertoires of proteins to chew up and metabolize their nutrients But after all of that they still double once every hour Does that make sense? That's a scenario. Okay, so Microscopically these are very different, but macroscopically they're identical So these cells grown in these two media Indistinguishable they have the same mass per cell. They have the same RNA per cell. They have the same DNA per cell By any macroscopic measurement you can't tell them apart underneath the microscope All right any by any chemical Measurement either I mean they're indistinguishable and this should show you how remarkable that is it's what it's saying Is that the growth rate is in some sense a hydrodynamic variable some state variable that when you twist it you get Sample this whole state space, but the microstate might be very very different So something like energy and thermodynamics Okay, but more than that you can look at say things that double twice per hour or things that take two hours to double and things like that And you can look at the growth rate dependence of these quantities and what you'll get is something or what you find They found is the following even more interesting. So there's more than this if you look at the DNA per cell Well, let's do mass per cell first Mass per cell and this is a log say log 2 of the mass per cell and this is now growth rate Then what I'm saying here is that triangle and square will have the same So they have the same growth rate and they have the same DNA per cell I mean if in an ideal world they'd be right on top of each other and they might well be I'm just giving them a bit of Scatter so you can distinguish them, but more than that is you arrange the growth rate or maybe this should be the doubling rate Just so that we get the base is the same so doubling Rate if you look at the slope you get almost a linear relationship, and I'll show you the real data in a second And in fact this mass per cell Scales like to to the growth rate So there's a lot in this figure. So let's see let's sort of pull it apart So the way that I'm going along the horizontal is that I'm putting these cells in balanced growth And then I'm looking at their number density as a function of time on a log linear plot I take the slope of that that gives me the growth rate. So each one of these dots is A day or two of experimentation Counting cells as a function of time and then there are 20 of these dots So, you know it takes a month or something to do this experiment And at each point you measure the growth rate and then you also take a sample And you measure the number of cells that are in that sample and the dry mass of that sample And then you take the reciprocal or the ratio sorry and as a function of growth rate you get this exponential relationship Does that make sense? I mean not not why it's 2 to the mu, but what I have plotted here. Is that a sensible? Okay, so now if we look at the RNA per cell again growth or doubling rate It's steeper. Oh, here's here's triangle here's square This guy now is about one and a half times mu and it's more or less exponential I'll show you the real data and this one now. I'm looking at the DNA per cell And this is again double rate and it's shallower and so it Proportional to say zero point eight times a double Okay, so there are a few things that I want to draw your attention to we won't really have Any rationalization for this for a little while we need to look at two more papers first But again, we have these very characteristic growth rate dependencies in this cell composition So that now I can actually backtrack so when we're talking about growth yield It's almost impossible. You tell me it sucks in eight. I tell you what the growth yield is But here you tell me that the cell is growing two doublings per hour I don't care what you're growing it in I can tell you what the mass per cell is average the average RNA per cell and the average DNA per cell These are like ideal gas laws if you like Okay, they came to be called growth laws. I'll show you the data here. Okay, so the real data is here So mass per cell RNA per cell DNA per cell you can see there's quite a bit of scatter and an exponential fit is You know What would you call it optimistic? Perhaps? The dashed lines don't worry about those those are chemostats and who knows what was going on But the solid lines are what's important These are batch growth like we talked about last lecture growing them in a flask stirring them up We're counting things chemistry basically So the horizontal line is biology the vertical line is chemistry All right, let me pause any questions. Yeah Yeah, no, no, it's exactly the same. Thanks So so last time we were talking about how to count cells Where will you plate them out? And then if they grow up you can count them and then back calculate based on the dilution to the To the number density that you had in your test tube and so you would express it and say Millions of cells per milliliter for example would be a way to measure that So here what you would do to get the RNA or the DNA is you would take a sample again And then you would measure how many micrograms of RNA were in that liquid Just chemistry and so you would get micrograms of or milligrams of RNA per milliliter And then you take the ratio and you get yeah, yeah, yeah So we knew what the mall we knew that there were molecules That are these long long sugars, but we didn't know what they did So that's a great point. So we know that the cell has this certain chemical makeup No, it did the there's a lot of work done by Germans at the beginning part of the 20th century Working out the details of for example the the Krebs acid cycle and things like this So we know where the molecules are, but we just don't know how they work We don't know what DNA. So remember this is 1958 Okay, no, so by 1958 we know that DNA is a hereditary molecule And we know that it it carries some hereditary information. We even know that it's got a double helix structure RNA we don't really know what's going on at this point. We won't know for another two years 1960 but we know that these are we know chemically that these are there Sorry. Yeah, so we know their chemical identity not their biological function Mostly for RNA. Does that make sense? And so his other question is how do you get the vertical axis? It's just chemistry. You measure you measure the you know by various tests the micrograms of RNA per milliliter Or micrograms of DNA per milliliter. All right, let me pause any questions. Ah, yeah, yeah Yeah, it's because it's very difficult to find a growth medium that will They will fill this void So that's partly why people liked chemostats in the early days because you could you could in principle sample continuously along the line, but They bring their own problems So yeah, so so it would then take a lot of ingenuity to try this try that to find precisely the right one That's one of the challenges of batch growth other questions. So the physicist you might be You might be worried about this Do you see any problem? Yes Yes Yeah, yeah, yeah, yeah, okay, so this is a this is something unsettling to humans for reasons that I don't know I also find it weird that what this is saying is that on average faster growing cells are bigger and I think that's counterintuitive, but I don't know why it is I Mean, I know why it's bigger, but I don't know why human how why we have strange time with that I have the same problem with daylight savings time. I don't know why it's so hard to figure out But I have trouble every year So the mass per cell this is saying that fast growing cells are bigger and they are demonstrably larger If you have a cell that's growing at say one doubling per hour And you have another cell that's growing doubling every 20 minutes. There's about, you know There's a four-fold difference in the did I do that, right eight-fold difference There's an eight-fold difference in the in the size of these two cells four-fold four-fold and So if you mix these cells together and you look at them under the microscope They look like two different species one of them is tiny. The other ones is gigantic long rod All right, that's very strange It would be good if nothing else comes from this course remember that because it's almost inevitable that That you come across some biophysics literature where the resolution is that one guy was growing cells Slightly slower than the other guys and that's why the sizes are so different What happens all the time? This is something that people seem to have forgotten Okay, so that's that's that's strange observation number one strange observation number two is When we have a tendency as quantitative people as physicists primarily to check units and the units here are bananas There's it doesn't make any sense But if you're gonna take An input to a transcendental function it best not have any units But he's because it doesn't make sense. There's no dimensional consistency here. So everybody see what I'm saying Right, I'm I've got two raised to the doublings per hour Doesn't make sense. I mean it fits a data But there's something weird going on here. The units are funny So I mean the way the engineers would get rid of this is that they would put a they would put a little fudge factor up There that has the same units And they say ah there take care of it And so the fudge factor here would be something that's one doubling per hour, but I mean that's fine It takes care of the dimensional consistency But why in the world should one doubling per hour have any magical significance? Why should that be the characteristic time scale? I mean one hour is a bizarre enough measurement for humans. Why would it have anything to do with E. Coli? All right, so this bizarre that's bizarre number two So the first one Well, why I mean, okay, tell me why yeah, yeah, yeah, yeah, it's true I mean it could be what if it was 80 minutes? It would still be bizarre But it's I think weird that it happens to be I mean it turns out there's gonna be a coincidence But it's a strange coincidence that 60 minutes is the characteristic time that we also use as a characteristic time Ours is totally arbitrary. This is also totally arbitrary and yet they seem to be Coincidentally arbitrary I think that's weird, but you're right. I mean if this was happened to be 40 minutes. It would be no less bizarre right You'd add you then again ask yourself was so special about 40 minutes Right, so maybe that's how I should have phrased it. What's so special about maybe the hour was was sort of a red herring But asking why what where is this characteristic scale coming from? Yes, yes, exactly gets rid of the problem with the units But but then that introduces a characteristic scale and then you have to ask yourself. Where does the characteristic scale come from? Is it does that make sense? I mean you could equally have chosen You know to make this guy unit list and then you would say okay Well, where does 40 minutes come from or whatever? But the point is that there's a characteristic time and we don't know what it comes from but we will in Maybe not today, but maybe an hour from that Okay, so these are two These are two insights that are not immediately apparent from this plot This is a lot of magic going on first of all. This is bizarre I mean the physicists not so much because you've seen this before where you have Degenerate states that give you the same macroscopic observables So you have you can have you know and a huge ton of different micro states that give you the same pressure for example They all have the same energy give you the same pressure not a big surprise here for for biologists This is you know was shocking probably continues to be shocking. I'm not sure Okay, that these these cells inside the regulation is very very different but macroscopically indistinguishable Okay This guy There's not too much to say now because we have with these two things out of the way certainly fast-growing cells have more RNA And that the RNA content seems to be increasing faster than the mass content So there's really only one one thing to notice here, and it's the opposite thing to notice here is the RNA content increases More rapidly with growth rate Doubling rate then the mass in here conversely the DNA Tends to or increases more slowly than the mass per cell And so if you're going to take reciprocals for example if you had the RNA per mass This would be slowly increasing with doubling rate if you took the DNA per mass You would have something slowly decreasing with mass or with doubling rate, and so DNA content Less slowly or less rapidly Doubling rate, and so this was 1958 this set the stage and this has been described as the fundamental Well this and then follow-up paper as a fundamental experiments of bacterial physiology This this is blew the lid open. It's not obvious yet Okay, but what did come out of this was that growth rate is an important Tuning parameter an important macroscopic Macroscopic observable or state variable with which we can tune and it presumably these guys are also Important state variables in the description of our cell at this level Okay pause one more time many questions. Oh, I Don't know about tumor cell mammalian cells, but certainly for bacteria that grow like E. Coli grows like bacillus subtilis These they all exhibit this type of growth law That the bigger they are the the or the faster they are the bigger they are I Don't know about tumor cells One of the tricky things about tumor cells is it's difficult to toggle their growth rate I mean it can be done, but it's People don't seem to do it any other questions. Yeah Yeah Yeah, yeah, yeah, yeah, yeah, yeah, yeah, it doesn't make sense. I Will though. I promise you I'm not I'm not gonna I'm not ignoring the question It's shy strange right because because what is this telling you? I mean does it tell you that the genome is somehow bigger? Right. Yeah, right. What? Yeah. Yeah. Yeah. Yeah. Yeah, I I agree. Okay, so so This is I Undersold this this is really bizarre as he points out It does this mean that the these bigger cells somehow have more chromosomes Then then slower growing cells and if they did then as he says does that mean they're a totally different species? What is that extra DNA? It's all it's at this point Totally unknown and the reason that I chose 1958 to 1968 is it there's no answer to that until 1968 And and the answer is so elegant that it's worth In some detail, okay, but in 1958 or sorry in 1958. This is this is a state And so what I want to talk about now, what are we doing for time? Yeah, we're good. So what I want to talk about now is this relationship Which comes from another paper in 1960 that was done. I mean experimentally fairly Similar timing it just took a little bit longer from the publish and then we'll come back to an experiment that Helps to open up the the question about why this might be happening particularly why this one hour is Meaningful and what extra DNA could be? With the origin of that Maybe all right, but let me pause. Does anybody have any other questions or? What would you call it unsettled feelings Great great. All right. Let's look at this guy and again. Remember. This is all in balance growth. So these cells have been Growing in the same test tube the same flat Well, okay, not the same the same growth medium for at least 10 generations before any of this data is taken Okay, so it's worth taking a detour now so we take a brief detour to 1960 in 1960 and this is a paper by night heart and Megasonic 1960 and so they use it all together different bacterium called Aerobacter argenosis, but it's very similar to to E. Coli very similar to Salmonella Growsing your gut And so you can see there's a problem here not just of standard reference conditions, but standard species So after this then E. Coli became the standard, but if you repeat this experiment, I'll show you data from E. Coli of this experiment probably Wednesday or Thursday, you'll get exactly the same result that they get and So they're faced with this problem that we know what mass is sure we know what DNA is It's a hereditary Information of the organism, but we don't know what RNA is We don't know what it does. It seems like it's It's somehow related with protein synthesis. I mean you and I know what it does, but they don't 1960 It's it seems to be related to protein synthesis, but in some obscure way and so there are many theories out there one of the observations is that Growing cells have more RNA per cell than non-growing cells But then already you start to say what you mean by growing and on growing It's not a well-defined situation and that's precisely their point as well The other point is that it seems like as you measure the amount of protein You also get it and you see a rise in protein synthesis rate You see a rise in RNA synthesis or RNA content, but the relationship is not clear and as I say one of the Theories is that RNA is used to make proteins in a stoichiometric way So every protein has its own piece of DNA which has been bound up with the protein and that's the active molecule There's a competing theory that maybe these RNA are templates for protein synthesis But there's no way to distinguish between these two theories at this point in time All right, so then night heart of magasinic come on the scene magasinic is in at MIT and he's physicist by training biochemist by By vocation if you like and night heart is is one of the great bacterial physiologists. He just recently passed away And so together there were in night heart at this point is a postdoc So instead of of doing what Schachter did They are looking at only the the ratio of RNA to protein So they look at the ratio RNA To protein in a whole bunch of different growth conditions. So again balance growth and Then what they do is so they did you know ten generations and balance growth And then they take a sample measure chemically the amount of protein per volume and the amount of RNA per volume And then they take the the ratio of that and what they see is a following. So this is now Let me switch to exponential units Or exponential base because I want to do some mathematics here And here I've got the RNA to protein ratio and what they see is if the growth rates high enough That ratio is linear But as you start to go to low growth rates, it sort of saturates out okay, so I'm trying to remember now if I put that data right after this. I probably did. Oh, I did good Let's think good thinking. All right. And so You'll notice a difference between their plot of my plot is that they've they've they've flipped it And I'm not sure why but if you if you put it this way, so if you just flip it along the XY line You got growth rate going here are native protein ratio and after about point Six specific growth rate it starts to go linear And they've got a pretty restricted amount of data here But this will go all the way to two to three doublings per hour for example, okay Is that that sensible? I mean it not why this happens, but is the data is it clear what they're plotting all right I'm going to give you one more piece of information and then I'll tell you their conclusion so also This is this is total RNA, so this is all of this chemical in the cell but they found that 85 percent of the total RNA is Ribosomal RNA So they didn't know what ribosomes were for another ten years But they they noticed that some of the RNA when you extracted it from the cell always always came with a bunch of proteins Strapped on to it So there was RNA that came out and then there was these RNA protein bundles that they called ribosomes Okay, and 85 percent of the total RNA was in these bundles irrespective of growth rate and their conclusion Was that these ribosomes? Synthesize or catalyze the synthesis of protein And they say that just as a sentence There is not a single equation in the whole paper and it's meant to be you say oh, yeah, oh, yeah, of course I mean that makes a complete sense. I Think to I don't know why I people must have been You know sensitive to this in those days, but I can't figure out how they would have expected the reader to understand that argument So we'll go through the mathematics But their argument is that this linearity coupled with this observation Tells you that ribosomes must be playing a catalytic role in protein synthesis that is to say that the rate of protein synthesis is Linearly proportional directly linearly proportional to the amount of RNA in this cell Okay, and if that gives you a headache, let's go through it in a little bit more detail But that's their argument. Okay, so this is the data Let me pause though any questions about the data Yeah, here here Yeah, okay, so We'll focus on here here the deviation will come to on probably Thursday Thursday or Friday and it comes from the The way these ribosomes work is they bring in amino acids And so that that process becomes limiting at slow growth And so your translation rate the rate at which these ribosomes make protein Slows down the rate per ribosome slows down That's not obvious, but that will come to that Any other questions? So we'll focus on this part here What night heart and magasinic called moderate to fast growth rate Oh, I should say also that they said this observation that non-growing cells and growing cells have growing cells have more RNA than non-growing cells they said is goofy There's a continuum of of RNA abundance. It depends on their growth rate And so it's not that they have more it's that they have linearly more Understandable. All right, so let's look at the origin of this. So from this they conclude ribosomes catalyze protein synthesis So at this point in time 1960, there's no way to visualize that I mean this is a deep level of inference from fairly high-level data All right, and so let's look at the mathematics So so they've immediately argued against this idea that RNA is consumed in the reaction Okay, so This is sort of going to be the first mathematical derivation of the course, but it's it's it's so pretty It's it really ties together a lot of ideas One is this notion of balanced exponential growth and in one is this this way that we infer Mechanism from from high-level information like this. Let's take a look So everything is in balanced growth. So we're in balanced exponential growth and so that means that you know that Cell numbers Increase exponentially that's no surprise But everything inside the cell also increases at the same rate this exponential rate and so as does every other other Component of the cell right the DNA if you did DNA the rate of Increase of DNA it would be linearly proportional to the content of DNA and that proportionality would be the exponential growth rate for everything balance growth imposes huge constraints and so in particular The protein mass. Let me call it m sub p Increases like this Okay, no surprise here. I mean I'm deliberately sort of going slowly Okay, again, it's exponential growth which mathematically is so simple, but biologically so deep That everything is increasing clockwork at the same rate. All right now. Here's the insight Where does that protein mass accumulation come from and the and the proposal by Night-hearted magasamic is that this is proportional to the action of these ribosomes and so this is some This is some Translation rate for ribosome and then this is the number of ribosomes Okay, and so by translation rate. I mean these ribosomes are putting together Say 20 amino acids per second per ribosome, and that's where this mass accumulation is coming from. All right, so that's there No, I've run out of room. All right, all the races. Okay, so does that proposal make sense? so you've got the rate of of protein increase Cut this guy out is proportional to some rate per ribosome of synthesis times the number of ribosomes in the cell That would be the the hypothesis if ribosomes were playing a catalytic role And so then now they they say well, I know that the ribosomal RNA is Constant fraction of the total RNA Now if I assume that the ribosomal RNA content of each ribosome is fixed which makes sense I think so if each ribosome has fixed amount Fixed our ribosomal RNA content. Maybe it's worth this to erasing this and the total RNA is You know proportional to the ribosomal RNA Then you can replace that number of ribosomes by mass of total RNA Then what do you have you have the number of ribosomes is going to be proportional to the mass of Ribosomal RNA, which will be proportional to the mass of total RNA is that string of proportionalities makes sense and You can figure them out from a biochemistry sensible then that relationship becomes this then You would have this DMP DT is equal to lambda MP and then I'm going to use some new proportionality constant because I don't know what each of these proportionality constants is but Proportional to the content of mRNA That is to say they're using RNA as a proxy or a readout of the ribosomal content of these cells And they're allowed to do that because they know that this string of proportionalities is fixed Across growth rates. It's always true now watch. This is just extraordinary All right, it's in steady state So just keep this part What do you end up with you end up with this m or mass of RNA per mass of protein is Going to be equal to growth rate times some k hat which is a straight line I mean theirs doesn't go through the origin. We'll talk about that in a couple of lectures But the interpretation here then would be that the slope of this line is telling you the rate per ribosome of protein synthesis It's extraordinary. So you get two things you get this this Hypothesis if you like the ribosomes catalyze protein synthesis, which we now know is true And in fact in the years that followed people Reconstituted protein synthesis in a test tube using ribosomes So they fed ribosomes amino acids and energy and they got protein out And so that was a direct proof of this hypothesis by knight hard and mega sanic Which comes down to this algebraic equation Very nice second of all you get this insight that if you just measure the slope of that line Provided, you know these proportionality constants You can estimate how fast ribosomes make proteins and it turns out that it's about 22 amino acids per second incredibly fast These are very efficient catalysts All right, let me pause. That's the first math of this Is it yeah, this is the front as a purpose is the first math of this of course we can take it slow. Yeah Yeah, yeah, yeah, okay, so so No, it's it's a question of the the regime that you're looking at so here was That Mikaela's mentum that we talked about Minot's relationship all of these experiments have that the yes is much much bigger than the KD So this guy disappears and you're you're operating at the maximum the saturated It's only Minot who pushes down to these slow growth rates Everybody else wants to keep these cells growing as fast as possible and at medium without their growth rate changing So if the concentration is too low, then they start to change the concentration as they grow And you start to change the growth rate and you don't want that so you put all the nutrients to high access So that they so that you're always in the saturated regime of these kinetics Does that answer the question Well, you would suppose you used This one and you put it here. Is that okay? So you've got lambda max to all of this, but then you knew that in your test tube this s didn't change Then it would just be some constant. That's fine. You just absorb it into the to the problem You'd be okay You wouldn't know what the you wouldn't know precisely what the translation rate was because you would have this confounding constant in front So make sense, but if you manage to push this as high as possible So you would just add more and more and more and more Run the experiment again and again again until you saw that the growth rate didn't change Then you would know that this constant was exactly the or you would hypothesize that it's the catalytic rate of each ribosome So it depends on how you manage your regimes, but you can always experimentally decide whether you're in that regime or not Does that make sense? So it's like if you're doing numerical methods, you just double the grid size and see if anything changes Or you have the grid Any other questions? So again, this is this pre predates any direct verification of this hypothesis But it gave people the the momentum in that they needed to start doing these types of experiments And it wasn't long before they as I say reconstituted protein synthesis in a test tube. All right Yeah, let's have a break but one thing that I want to mention here No, you know, we'll do it after the break Yeah, why don't we take a five-minute break or however long it takes to go back in? so So with this this relationship in 1960 There are three points that I want to make that are beyond this. The first is that this this is true I mean empirically true that you get this near linear relationship at fast enough growth rates That suggests that you have this coupling between growth rate and and ribosome abundance, but then immediately Scientifically you ask yourself, where does that come from? How do you ensure that that happens? And so as soon as as this published this work was published in 1960 it inspired generations at least two generations of Biologists to search search for regulatory mechanisms that would make this happen. And so So some of the outgrowth consequences Here are One how do you regulate? I mean this is this is a correlation, but how do you cause it to happen? How do you regulate the growth dependence in This ribosomal content and many people have worked on this so I'll just give a short list no more as a big player Hans Brammer Rick Gorse Many others and the answer is that it's still controversial these guys all argue with one another while the more is a Doesn't argue as much These guys these guys will argue with one another about what the mechanisms are that ensure this growth dependence So still controversial and this is so now 50 years ago to How do you ensure that this is true? Did you maintain this stoichiometry between the ribosomal RNA and the ribosome content? Because what you find is that there is very little free ribosomal RNA floating around. There's almost no ribosomal protein floating around Okay, so how do you ensure? Do you keep? the RNA content of The ribosome a fraction of total RNA a constant across growth rates and this was unequivocably answered by Nomura, and I'll say a couple words about that because it's so elegant So what I'm asking is if we know that the total RNA is is 85 percent ribosomal RNA And we know that there's some certain stoichiometry in the ribosome so for example Free Coli the E. Coli ribosome is two grams of ribosomal RNA To one gram of ribosomal protein So it's two-thirds of the mass is ribosomal RNA and one-third of the mass is ribosomal protein So you can think of these ribosomal proteins as little tiny structural proteins that are holding together giant tangles of ribosomal RNA But you never find ribosomal RNA free and you never find ribosomal protein free Somehow and there are 53 ribosomal proteins 54. How do you make sure that these guys all come together all the time in concert? Everybody see the problem That's so the genius of Nomura and this isn't a side I mean it's not really part of what we're focusing on here because this took 20 years to figure out But when Nomura found was it ribosomal proteins are obviously very good at binding to RNA So what they do is they bind to the mRNA the message RNA that makes those proteins and shuts them off So if there's any free protein floating around it pins down to its own Message RNA and stops protein production of ribosomal proteins It's very clever So this was answered by Nomura. Nomura. This is still not unequivocably answered But then the third point that I want to make is that and this is something that we appreciate now in hindsight Is that if you want to make more ribosomes? You need to make more ribosomal protein and if you make more ribosomal protein you need to make less of something else And so although you do get this linear increase in the ribosomal content with growth rate That comes at the expense of making linearly decreasing levels of some other protein All right, and so that's the last point I want to make and we'll come back to that on Thursday probably so the third point that is is To make more ribosomes ribosomes in rapid growth we necessarily Make less of some other protein Okay, and I'll talk about that constraint in much more detail after we've talked about these historical papers Just historically this is this is at least three consequences to come out of this very Elegant but small study by night heart of Megasonic in 1960. Yeah So To visualize them so so the question is when were they actually able to visualize this process of ribosomal? Translation there there were electron micro Micrography so they could do electron micro so they couldn't observe it in real time But they could free cells cut them open and then look at they would see it sort of a squiggle molecule And then a bunch of little black molecules that were the ribosomes So and it looks sort of like a Christmas tree. It's a really spectacular picture But that's not I mean, it's not quite the dynamic picture that's here that Yeah, we'll probably take till the 1980s mid 1970s. We'll talk about that probably in in a few lectures It's okay Friday problem Any other questions? All right, let's look at the last last paper of 1958. Oh I didn't pass around the sheet. I'm gonna pass around the sheet now if you know Let me guess this so now we go to the second paper of 1958 so this one is Same three as the first one But now Kuhl guard gets first billing and this is growth transitions So so far we've been talking about steady-state balanced exponential growth Now in this paper what they're going to look at is something that's growing in a slow Growing slowly in a particular growth medium and then they add two times concentrated fast growth medium and Then the cells sort of take off and then the question is what happens to all those things that I showed you After a transition so they look at two different types of transitions. So they look at a shift up Which is one that I just described and a shift down But the shift down is much less clear What's going on and that that's partly because you need to make new proteins to be able to consume these these poor growth medium? Poor nutrients, so look at this All right, and so let me sketch what they see Bless you It's probably best to do it big on a big scale And so this has been described by Sukchun Jun at UCSD as a as a prism So the growth transition takes place here. It's zero They they change the growth medium or they add a richer growth medium and the cells start growing at a different rate and all of these constituents then split up so the RNA per cell the DNA per cell the Number the cell numbers these all change to their new rate their new exponential balanced growth at different times after this shift Okay, and I'll draw it in an idealized way so that you can see what's going on here so this is log two of whatever you can think of it as X per milliliters if you like and you've got something that's growing at Some particular rate and Like they've done I'm going to separate these two lines Even though these two lines could be right on top of each other just so there's clear what goes on This is t equals zero, which is the time of the shift the RNA per cell Transitions discontinuously as fast as you can measure it. It's already at its At or above its new rate of growth. And so this was the first growth rate Mu one and this is a second growth rate Mu two and mu two is Much much bigger than you want in their case. It's about double. So it's not hugely different. Yeah So say you've got medium a that it grows slowly and they've got medium B that grows fast in they made this twice as concentrated And then just dumped it in and then it is basically medium B immediately Make sense. All right. And so this is a rate of growth of the RNA then you transition won't the RNA goes up like this you wait about five minutes and then the Mass per cell starts increasing So this space here is How I do this This thing here is T mass is About five minutes and then you keep waiting and you'll get the DNA Increasing here after about 20 minutes. So here. This is T DNA It's about 20 minutes So that's the top three Lines that they've got written here. They write optical density because they're using that as a proxy for mass But mass is easier to imagine and in a long time after 70 minutes later Cell numbers starts increasing. So this is meant to be one continuous line. So this now is T cell is About 70 minutes. So let me let me summarize and then let's go through it. So one The order matters. So you get T RNA Which is like essentially minus five minutes if you want to keep this continuous is less than T mass Which is less than T DNA Which is less than T cell so I sense T RNA is basically not I mean you can even not imagine it's a discontinuous shift So you can leave it out if you like And then there's also the timing so the timing is That T mass is about Five minutes T DNA is about 20 minutes and T cell is about 70 minutes and what they found was that it didn't matter What you started with and what you finished with those times were always the same times irrespective of Where you started me one and where you finished you to all right and then the other point that I want to make Oh, yeah, is that these shifts are basically Piecewise linear on a log scale, which means they're piecewise exponential Okay Those are three observations that you can make from the graph that the inset here is the DNA content per cell And so as was mentioned before These guys go from having what looks to be about one and a half chromosomes to having three chromosomes per cell whatever that might mean Okay, we'll come back to that obviously Okay, so these three observations are the ones that I want to draw your attention to does anybody have any questions about What I've written here Hopefully, can you see from the data that my idealization is not too far off? I mean their lines are better drawn in mind obviously But that the data is not far off from the cartoon figures or the line fits that I have written or they have written Okay, now really So I think on the face of it This looks puzzling Why should these times all be the same or yeah? I mean they're not same among each other, but I mean why should T cell always be 70 minutes afterward Why should have nothing to do with these growth rates? That's bizarre Okay, that's bizarre Observation number one Bizarre observation Number two, I can't remember now Anyway, I'll think of it again. So that's strange. Why should this timing always be the same? And what Mola noticed and what will go through for the next ten minutes is that actually you could have predicted this from the steady-state data And that is not at all clear Okay, or better said from the shift data, you could have inferred what happened in the steady-state All right, let me pause though again as the data clear Okay And so Mola's claim and this just is an example of how quantitative Mola was Mola's claim These timings these times are Implicit in the steady-state data So those growth laws that I showed you at the beginning of the lecture Where they had the steady-state mass per cell and so on All of those relationships are buried in these timings as I'll show you in a second. Yeah. Yes, that's right Yeah, no these guys are per volume These are per volume. Yeah, and then you would take their ratio as per cell to get the we'll do that though We'll take the ratio in a second so this is log base and per volume per, you know milliliter So this is bonafide chemical content of your test tube. I Remember what I was going to say this separation of time scales to Mola suggested that these are all independently regulated events Whatever's regulating cell number ie cell division is an independent regulatory process from what's the Dictating DNA for example So his argument was if they were the same regulatory process, they'd be they'd be kinking at the same time See if you agree with them. It doesn't he suggests that this decoupling is a decoupling of regulation as well All right, let's see why Mola says this Okay, so I'll bring you back to Say mass per cell and this is doubling rate and what we had was that this is something like two to the mean and now Mola's observation is that You go from growth rate one to growth rate two You slide along that line Who cares about the transits you go from here at and then at t zero you shift up to here It might take some time to get there But the slope of this line is exactly the amount of time it takes you to change and again That's not obvious and we'll go through it in some detail And so what he's saying is it because you have this exponential or this linear relationship on a log scale You would expect that these times are all going to be well relatively the same It the easiest hypothesis is that they'll stay the same So let me show you how he gets that All right, let's take a look. I can erase that this right and so let's let's go through this In some detail. So if we're looking at for example the mass per cell, I'm going to call that M2 of t so that is In or this is the mass per cell at growth rate Or doubling rate Mu 2 then this is going to be the ratio as you said of the mass to the number of cells going to be the mass To the number of cells at you know again growth rate to right does that make sense? And so what we're going to exploit is that these things are increasing exponentially and that they are piecewise exponential that their their shift is so abrupt that they're basically Linearly what you call a piecewise linear on a log scale Okay, it's going to take a little bit of fiddling, but it's not terrible. All right, and so in the In the rich medium, so long post post shift You'd have this M2 of t is equal to some you know M2 of t which I have written here, but I'll write it out in this more detail M2 given by this to to the M2 or Mu 2 t minus t mass. I don't think that's visible to to the mu 2 t minus t mass Okay, that's this line right here So I know the slope is mu 2. I Know that it transitions at this time t mass And then I also know that this initial point here is going to be M1 M1 at t mass That is to say it follows the first growth rate Until it reaches this This transition time about five minutes later. Okay, let me pause So what's buried in there is that the shift is is piecewise exponential I'll show you where that comes in the second and then the second part is that it grows exponentially at the new rate immediately after this shift Does it make sense? Do all the symbols make sense? Okay, we can do the same thing down here. So the end is going to be N2 is going to be now n1 at t cell times 2 mu 2 t minus t cell so far so good now we'll Mix it around so here these these pre-shift rates So these are pre-shift are again in balanced exponential growth They're growing with this doubling time of mu 1 and so they look like this Mu 1 at time 0 or m1 and 0 times 2 to the M1 t 2 times the m1 t That's to say these guys are both increasing exponentially at some given rate with some initial condition. Does that make sense? So now I can substitute that into those expressions over there and it's going to be horrendous I'm going to have a ratio of a bunch of exponentials multiplying one another But they'll simplify in a very nice way, which I'll show you in a second But I want to make sure both both halves of this con this calculation are sensible. Are there any questions about it? So these are the post shifts Everything's growing at mu 2. These are the pre-shifts. Everything's growing at mu 1. Let's bring it all together So then all together This will take just five minutes. So then all together this M2 at time t is going to be this M1 0 over n 1 0 these initial conditions times 2 mu 1 t mass Times 2 mu 2 t minus t mass divided by 2 mu 1 t cell Times 2 mu 2 t minus t cell and let me take a step back Okay, this is the piecewise exponential That dictates the mass and this is a piecewise exponential that dictates the number And I take the ratio so far so good now this thing is going to tidy up very well very nicely because of This 2 mu 2 to the t 2 mu 2 to the t That is to say that post shifts when it comes to equilibrium their rates are the same as They should be because it's in balanced growth And so this will tidy up So in balanced growth first of all this guy mu 2 of t becomes a constant or this M2 Sorry becomes a constant Second of all this M1 Or this this ratio M1 0 over n 1 0 is a constant That's what we mean by balanced growth and those two exponents cancel so that Let me write it up and then let's talk about it so that we get a constant equals M1 2 raised to the power t Cell minus t mass times the difference of these growth rates mu 2 minus mu 1 Like it's very nice I mean, it's not super nice yet. We'll see that it's going to be very nice in a second Okay, but so far so good. Is that calculation? Okay? It's the rules of exponents basically and this constraint that we have balanced growth much is Now if I take the logarithm of both sides So I take log M2 is going to be log M1 plus This now t cell minus t mass Mu 2 minus mu 1. Okay. These are base 2. I can tidy this up a little bit I'll move this over to one side and I'll call this delta log 2 Delta log 2 of the mass Meaning the difference in the logarithm of these mass per cell at growth rate 2 and growth rate 1 and That's going to be equal to this difference t cell minus t mass and I'll call this the delta growth rates delta mu. All right. Why do I do that for the following reason? So let me write this last piece up and then let's talk about it and again. This is the last thing we'll do today, so Bear with me for two minutes or This delta log base 2 of M the mass per cell divided by delta mu is equal to the difference in times t cell Minus t mass. All right, and then let's go back to the steady state So this is mass per cell log base 2 This is the doubling rate. What's this slope then? What's that? Exactly right. So this is telling you that the slope of this line Which we know to be one doubling per hour is going to be this difference in times Okay, and so this slope here we know so we know that this thing is like that And so out in front here. We have one hour per doubling divided by one hour per doubling But the implication from the shift data is that the slope is going to be t cell Minus t mass. Does that make sense? So that's all of this calculation again. Mola left this unstated It was implied just by the words. Oh, we had one figure, but it's very obscure How does it compare? Well, if we now look at these guys we end up with the t cell is about 70 minutes minus five minutes It's about 65 minutes The slope up here is About 60 minutes It's an error of about 10% on the other hand It's very hard to tell where the kink in this line is could be you know, maybe 60 maybe 65 It's not a bad estimate and it's a self-consistency check Now if you look at the DNA per cell you do the same calculation the DNA per cell it has a a Slope of about 48 minutes. I think is 48 minutes From the steady state and it's about well, we can calculate it 70 minus 20 which is 50 minutes From the shift so it's extraordinary level of agreement. It's like within 5 to 10% and again It's a self-consistency check and in retrospect now It doesn't seem miraculous that the timings are always the same because you end up with this straight line relationship for all Doubling rates more or less That's extraordinary really all right, and so then one question that we had was why are our cells bigger faster growing cells bigger? It's because it takes 70 minutes before the numbers start to increase Okay, that's not really an answer. It's just pushing the question to another question Which is why does it take 70 minutes for this guy to start up and we'll answer that? Tomorrow or Wednesday, okay, I don't know when when the timing will work Okay, let me pause is any anybody have any questions. So here we have a brilliant piece of self-consistency between these two very different experiments Steady state exponential growth and shift experiments We see they match up very nicely and The question is why right? Okay? I'll see you guys tomorrow