 Keep it up. It's OK? All right. OK, well, thanks very much, Jakopo, for having me. So I work in Basel here. This building is our, oh, God, this is difficult. This is the new bio-centrum that we just moved in one year ago or so, and this is the group. All right. So the topic of today's talk is E. coli's amazing versatility. As most of you know, a simple organism like E. coli can adapt this gene expression to really an enormous range and combination of environments or changes in nutrients, in different stresses, temperatures, pH, osmotic pressure, and so on, and so on, and so on. And these can all be in large numbers of combinations, and somehow it finds a way to adapt this gene expression to grow in all these environments. And the traditional explanation of how E. coli does that is, well, E. coli has all these sensors and regulators that form these complex regulatory networks. Like here's a picture I stole from some review. And basically, these sensors measure what kind of environment E. coli is in. And these sensors are then coupled to regulators that set the gene expression levels, and there is this complex regulatory network that is there to basically control the gene expression of all the genes. And it is indeed true. So this is some very ancient work, which is showing that as you go to larger bacteria, the numbers of sensors and regulators is growing disproportionately. So the numbers of sensors and regulators that a bacterial genome of size G has grows as G squared. So this is saying, yes, see, if you have a bigger bacterium with more genes, it can live in more environments. And so it needs all these regulators and all these sensors to be able to set expression levels. And so the idea is, the picture is that through evolution, bacteria have learned what the correct combination of expression levels is in each environment. And that basically, this regulatory network has then been designed by evolution to make sure the cell will set the correct expression levels in each of the environments. So the first thing I want to convince you of is that that picture cannot be correct. So it cannot really work like this that E. coli has simply learned through evolution to sense, where am I? Aha, I'm in the gut of a human, or I'm in the sewer. And that means I have to set my expression levels like this because evolution has taught me, these are the right expression levels for this environment. So what are the observations that challenge this picture? So the first thing is that if you, all right, so many molecules in the cell are at low copy numbers. So in particular, the DNA is typically at one or two copy numbers in a cell. And so when a gene expression event happens, a transcription event, that's a single molecule event that happens at a single molecule in the cell. And because there is just thermodynamic noise, the cell cannot, say, make one transcript exactly every minute. The only thing that the cells can control is the rate at which various reactions happen. And so even if the rates of reaction are constant, so if you have a constant rate of transcription translation and decay, then the CV squared, so the variation in the number of proteins you're going to get, if this thing were to work, is basically going like one over the total number of protein, all right? And so if we now look at what is the distribution of the total protein count, so this is being measured about a little over a decade ago by Taniguchi at all, you see that actually most genes in E. coli typically have less than 10 or less proteins per cell. OK, so most genes, this number n, the number of proteins per cell, is low, which means there must be large variability from cell to cell. Most genes, even if all the rates were constant. Of course, in reality, transcription translation and dilution will fluctuate in time from cell to cell, and these rates will depend on binding and unbinding of transcription factors and RNA binding proteins and so on. So these rates will also be all stochastic. So in general, the stochasticity will be even bigger. It's like a lower bound. Now, these low copy numbers, they also apply to sensors. So many of the sensors are these two component sensors. And here is from some proteomic study from Alex Schmidt, the distribution across different environments of the numbers of copies that these sensors have per cell. And again, what I just want to focus your attention to is that many of them in a lot of environments have less than 10 copies per cell. OK, so these sensors are also present in low copy numbers. And there is this old seminal work of Burke and Purcell that basically shows that the accuracy of sensing is also going like 1 over n. This is all coming from sampling noise, essentially. Right, this 1 over n accuracy. And so if at 10 sensors, the cell will basically have one bit of information about what the thing is sensing. All right, so it can tell this thing is not there or there's a lot of it, but it cannot tell there's a tiny bit or a bit more or a bit more. Yes? Just as a question to this sensing, I'm not a biologist, so maybe this is very wrong. Very good. My understanding is that cells don't actually feel the existence of something, but rather the flux. So like chemo-attractive, you don't feel the environment, but you feel the change. They're only attracted because there's a gradient. That's a downstream property of this network. But what's happening molecularly, and that's what this work per cell paper is about, is that there is a receptor on the cell, and there is some molecule, and it binds and unbind stochastically from this receptor. And the only thing that the cell senses is basically this time course of bound, unbound, bound, unbound, which is controlled by right to these molecules, they do Brownian motion. And that's where these bounds are coming from. But still sort of over time, right? They sort of integrate over a certain amount of time. It's not that at every time point you feel this, but... Okay, so... Or is that... There is like 40 years of work on can you do better than this? And essentially you cannot really do better than this. Yes, of course, you can do time averages. You can couple it to things that lies ATP, do sort of error correcting kinetic proof reading like things and so on. So we could talk about it for a long time, but the bottom line that I wanna make is that there is no way that the cell can tell its environment with high accuracy, given the low copy numbers. All right, so the summary of these points is that regulators and sensors are themselves also subject to expression noise, so this will make it even more variable. And so this says that the sensing and regulation that individual cells do must have low accuracy. And so the picture that I get from this is that cells are effectively stumbling around in the dark with relatively little information about where they are. All right, so that's point number one. The second point is something that I learned from Sydney Brenner about a little over 20 years ago and that really influenced my thinking about how these regulatory networks work. And that is that you can, that E. coli can adapt this gene expression to environments that are completely alien to it and they cannot have evolved to recognize it, all right? So what you can do is you can take E. coli and put it in fully deuterated water, right? So all the hydrogens in water are deuterium. And NMR people like to do that because they like to make versions of proteins with deuterium in them and so on. And the thing is eukaryotic cells all die when you try to put them in there, but a cell like E. coli, it will simply adapt. And this thing is a severe perturbation to the cells chemical network, right? So all the reactions that involve water in one way or another, they now happen at a completely different rate, maybe 10 fold up, 10 fold down, maybe even up to two orders of magnitude change. And somehow E. coli takes a while, takes a couple hours, but then you find that E. coli has adapted its gene expression state. Hundreds of genes have changed their expression levels, sometimes at very large amounts. These are often enzymes that are involved in these reactions that involve water. And it's found in a new solution in which it's now growing exponentially at only sort of half the rate that it would grow in normal water of the same condition. And the point is that evolution cannot have prepared E. coli for any of this, all right? So the way it's found the solution to the problem must be some generic mechanism. Cannot be something that's learning evolution, yes. Yeah, I was thinking about this example because it was mentioned in the talks before by Hugo, I think. But yeah, what if the cells could then nevertheless, okay, it cannot sense deuterium directly, but it could sense something which correlates with the deuterium. So maybe there are other parameters which change similarly to how other variables to which E. coli is accustomed to would change. And basically the cells just sense that and adapt to the change because if deuterium, if the water is a bit heavier, then probably some kind of rates will change, something like that. So the cell could still sense a, yeah. So I appreciate very much that you understand the puzzle, okay? And so I've been thinking about this puzzle for 20 years. And so I will try to give you what I think is ingredients to the answer to this puzzle, okay? So then at the end of the talk, you can tell me whether that fits with what you're currently imagining or not. Okay, looking forward to it, thanks. All right, so what might this generic adaptation mechanism be? So basically what I wanna do is I wanna go through some things, results from the last 10 years in my lab that I think are bringing together in my head at least a picture of how this might be working. All right, so the first ingredient for this generic adaptation mechanism is that growth rate through the effects of dilution sets the sensitivity of regulatory switches. I wanna actually spend probably most time on this part. Okay, can I stop this? No, of course I cannot. So we've been looking at a system which I, you know, I'd like to call the hydrogen atom of gene regulation, which is the lack regulatory circuit which is shown here. So there is this operon that has an enzyme for eating lactose. It has a transporter of lactose and one thing that it's still not entirely clear what it's doing. And basically the, and then this promoter is normally repressed by this repressor like I when there is lactose in the environment comes in through the transporter. Allo lactose, which is made by this like Z binds to like I inhibits it. That induces the operon makes more of this transporter means more lactose gets transported in. So there is this positive feedback loop. So depending on how much lactose in the environment this loop can go critical and induce expression and then the cells will start eating lactose. Actually it's this system that led to the discovery of gene regulation transcriptive factors, mRNAs and so on. And so this is sort of really sort of the canonical example of a gene regulatory circuit. And now we've put this in this mother machine. So you've heard about these microfluidic devices where cells are growing in a single file and now we're gonna switch them every four hours between glucose and lactose. And you will see now they switch to lactose. Everybody stopped growing. Some guys are still stopped, but some other guys are already inducing lactose and they're growing again. So the observations that we have when we do this is that when you switch to lactose the first time everybody stops growing immediately. Then there is a stochastic waiting period. Then cells start waking up. And as soon as we can see expression of the lachopuron they please grow. And upon later switches there are no more growth risks. Yeah, so this is in this, so it's even shown in this picture. So the GFP protein was added to lactose. So these are actually fusions of Loxy and GFP that you're looking at. Okay, all right. So now the observation that we made is that the distribution of lactimes is bimodal. So 30% of cells are fast and they go between 20 and 45 minutes. And then there is a second hump where two thirds of the cell go between, let's say 50 minutes an hour to three, four hours. And okay, so it's a long story. We looked at what determines whether a cell is slow or fast. But basically the answer is it's determined by pre-existing lach expression. Okay, and one of the ways that we know this is that we can manipulate this distribution by giving tiny amounts of repressor, of the lach repressor, this TMG molecule or IPTG that you can add to the cells. It basically turns off some of the repressors which even though the lachopuron won't be induced, it will increase a little bit of the leaky expression that happens when they're growing in glucose. And you will see, so if you add a little bit of inhibition of the repressor, you will see now you push the distribution to that now 50% of the cells is fast and if you give a bit more, 65% of the cells is fast. Whereas if you give lach repressor protein from a plasmid, so you make more repressor, now you can move that essentially everybody is slow. Okay, so how much is in the first mode and how much is in the second mode? You can change by changing the expression level of this repressor and this repressor is known to only target the lachopuron in E. coli. It doesn't target anything else. All right, so giving these tiny amounts of more of this repressor or less is not gonna affect anything else than the pre-existing expression of this lachopuron and that's why whether you're in the left peak or in the right peak is determined on how much pre-existing lach you had at low level when the switch came. Okay, so the question is now, how much lach do you need to have to make this feedback loop go critical? Okay, what is the critical amount? And so we did experiments where we induced the cells in lachos and then we grew them in glucose for a variable amount of time and then we switched to lachos again. And so when they're in glucose, they're no longer expressing the lachopuron. So what is happening is that the amount of GFP per cell in the amount of lach C is sort of diluting with time and because we're in this mother machine, we can actually track as it's diluting in time. So even when it falls below the detection limit, we can still from the growth of the cells in the divisions estimate how many lach C and lach Y molecules were left in this cell when we came back with the lachos, all right? And so then what you can plot is as a function of how many GFP molecules have you inherited from your ancestor that was growing in lachos, what is the fraction of short legs? And you see to go back to the original fraction of short legs around 30%, you need to basically go down to one molecule, all right? So the number of preexisting lach molecules that you need for this feedback loop to go critical is very small, all right, on the order of one molecule. So when these cells are sitting there, growth arrested, they're extremely sensitive. If they have no lach expression, they cannot detect lachos because it cannot even get into the cell. But as soon as you have one, two, three molecules of lach Y and lach Z, that's enough for this feedback loop to go critical. Now, the first time we saw this with work, we were surprised because we knew a paper from 2008 where very similar experiments were done where the conclusion was that the critical amount of lach expression for the feedback loop to go critical is around a few hundred molecules. So not a handful or one, but hundreds. Okay, this is a hundred fold difference. And so the question is, okay, where is this coming from? Well, the only difference between our experiments and these experiments is that in those experiments, they didn't really use glucose and lachos, but they grow the cells in glycerol and then they add different amounts of artificial inducer that the cells don't eat. And so in that case, the cells are always growing, okay? And they're giving this inducer while the cells are growing. Whereas in our case, the cells went into growth arrest. So what it suggests is that with cells that are in growth arrest, they're much more sensitive to the signal than when they're growing. So then the question is, can we understand that? It turns out, well, it's very trivial to understand that. So you take the sort of simplest models of this lachopuron, this is just a couple differential equations that this is due to a paper from Osbuduck at all in 2004. And we just adapted it to take into account that the internal concentrations of the inducer and of the transporter, they're given by a balance of, this is import and dilution, and this is production and dilution. And so basically the growth rate of the cells sets the rate at which these molecules are diluting because these molecules are very stable on the lifetime that cells double in size. And so basically what you find is that the critical point of this feedback loop is controlled by this dimensionless parameter, which depends on, so B here in the denominator is essentially the concentration of the molecule of lactose outside. A-L, A of lambda, sorry, is the maximum rate of production of proteins from the lachopuron at growth rate lambda. And then here is basically lambda squared because these decay rates are small. So you see that this essentially depends quadratically on growth rate. And so we decide, so this is basically the summary of what this very simple model says, the very simple model says, okay, so you have this positive feedback circuit and as a functioning of the doubling time of the cell and the level of the inducer outside, you basically get this phase diagram with an uninduced state and induced state and a bistable state. And you see that when you're growing slow, when you're growing, sorry, when you're growing fast, you need a lot more inducer to induce than when you're growing slow, okay? So we tested this and this very simple experiment to test, right? So this could have been done by Monod in the 60s when they discovered the lachopuron regulation. You simply grow E. coli in different environments where they grow at different rates. You add artificial inducer and ask, how much do I have to add before the feedback loop goes critical, okay? So this is what you see. So each line here is E. coli in it is growing in different nutrients that make it grow at different rates. And then on the x-axis is this artificial inducer. On the y-axis is the population expression of lactose. And so you get these induction curves. You can work out where is the critical concentration. And then you can plot the critical concentration as a function of dumbling time. And you see that it actually decreases a little bit faster even than quadratically, okay? So this is going from sort of a half an hour to four hour doubling time. And this is almost a hundred fold change in how much of this inducer you need to induce the feedback loop. All right. What time is it? How long have I talked? In 20 minutes. Okay. Okay, so there's something very cool. You can do it this, but I think I'm gonna first do the rest of the talk and then I'm gonna come back to it. I'm gonna skip this. All right. So basically the inside is that growth rate through dilution sets the sensitivity of these kind of positive feedback regulatory switches. And so this is a very general mechanism. So we expect this to occur for basically almost any of these regulatory switches with positive feedback. So for example, the sort of simpler system you can imagine is a switch that is really, doesn't have any input signal and it just switches as a function of growth rate. If you simply have an operon that contains a transcriptor factor that positively regulates its own expression, then you look at the phase diagram, you see that depending on what sort of the basal level of the operon, the basal expression level and doubling time, it will go from off to induce, to buy stable to induce. So you could, for example, imagine that a phage that might want to use such a system that it integrates itself in the genome and it stays in the genome as long as its host is growing fast enough. And when the host is growing slow, then this system goes critical and the phage says, I go litig, I get the hell out of here, okay? But many, many regulatory switches in these bacteria have this kind of architecture, that there is a positive feedback loop that is coupled to a signal, either through the decay rate of the regulator that is coupled to the signal, or many of these two component systems that bacteria use, they are basically the consist of a regulator and a membrane bound kinase that positively feedback on themselves and the kinase is coupled to an external signal. And so all these systems, they will have the feature that their induction does not only depend on the signal strength, but also on the doubling time of the cell and that typically the slower the cells grow, the more sensitive the system becomes to the external system. Okay, so actually in the supplement of the thing, I go through a whole number of these sort of architectures that you could set up and say, how is it gonna scale with growth rate depending on how you set it up exactly and so on. And I only scratch the surface of a couple of ways you can do this, you can build many, many, many circuits that can scale anywhere from not scaling with growth rate to like third order with growth rate or something like this, right? It depends on how you set up the details. Okay, so the summary of this is cells through dilution affecting the sensitivity of these regulatory circuits basically automatically are provided with this strategy that when life is good and they're growing fast, they're essentially muting the signals from their environment and not paying any attention to fluctuations of signals from their environment. And when they start growing very slow and life is bad, they become much more sensitive to signals coming from their environment and are much more likely to switch their stack, okay? So that's number one, okay? Second ingredient, gene expression fluctuations are driven by propagation of noise from regulators to their target. So we're now gonna look at gene expression noise. So one of the ways you can look at gene expression noise is to use transcriptional reporters, fluorescent reporters and use flow cytometry, put cells through a fox measure the amount of GFP in each cell and look at distribution. So luckily, lab of Urielon, so there is this paper from Sonslavor, they made a library where essentially they took every promoter in E. coli and put it on in front of GFP on a plasmid. So you can put these plasmids in your cells and then you can put your cells through a fox machine and you basically get a distribution of expression levels in the cells for the same gene. So these are isogenic cells growing in the same environment. And so we've done this extensively and basically for almost all genes, the distribution of expression levels is log normal, okay? So this is expression levels on a log scale and you get basically roughly Gaussian distributions on this log scale so you can characterize the distribution by its mean variance. All right, so now you can make plots. So here's a plot on the left where every dot is an E. coli promoter and on the x-axis, this damn thing doesn't work again, on the x-axis is the mean of log expression on the y-axis, the variance of log expression. Okay, so you see there's this systematic dependence between mean and variance. This is actually very easy to understand. It comes from, again, the Poisson noise of the production and also actually the Poisson noise of the fox machine because it uses a photomultiplier to measure these things so there is also a Poisson noise in that but basically there is one term here which dominates at large expression which is the sort of the true variation in log expression which is dampened by a factor that depends on the outer fluorescence of the cells and then there is this Poissonian term that goes like one over mean and that is coming from both the measurement Poisson fluctuations and the internal intrinsic noise fluctuations but so what you can do is you can correct for that term and then you basically get what is the excess noise above this lower bound on noise that each gene has. All right, so what we did in an early study is we've compared this excess noise of the native E. coli promoters with a library of synthetic promoters that we got by taking completely random 100 base pair inserts, putting them in front of GFP on the same plasmid so exactly same construct and then selecting out the subset that are expressing. Okay, so we selected guys by gating that are either expressing it sort of the mean of all E. coli promoters or at the 95% of sort of as high as ribosomal promoters and so those are shown in red. So there is basically a cluster here on the left, these are these mean expressors and the cluster here on the right is the high expressors and then on the Y axis is the excess noise and basically what we notice is that essentially all these synthetic promoters have low excess noise. All right, so if you take a random sequence and you select the random sequences that express they will all be low noise, okay? Now we check these promoters as far as I can tell these promoters only have binding sites for the sigma factor for the polymerase. So these are essentially constitutively expressed promoters. They have no regulation. So promoters without regulation seem to be low noise. So we managed to sort of confirm this by, now this is, we've measured, so Aransa, she measured the whole library in eight different growth conditions and measured the mean of variance of all E. coli promoters and basically you see that in every environment there is a good correlation between the number of regulatory inputs that a gene has and noise. So basically what happens here is we sorted all the promoters from all of them to ones with higher and higher noise and then we looked at the distribution of number of regulatory inputs and so this is showing the mean plus standard deviation of the number of regulatory inputs of promoters that have a certain amount of noise and you see that so the most noisy promoters are the ones with many regulatory input and this is true in every growth condition. Moreover, if you look at one promoter at a time and ask how does its mean and variance change across growth conditions, you find out that basically every promoter has his own characteristic way of changing its mean and noise across conditions. So it's not the case that some promoters are always low noise and some promoters are always high noise. It's that in each condition different promoters are more or less noisy. All right, so the noise levels of promoter are highly condition dependent and so these observations can be explained by saying that a lot of this expression noise, this excess noise on top of this lower bound is coming from propagation of noise from regulators to their target. Right, so the basic idea is that if you have this pink gene here that is regulated by the blue transcription factor and the blue transcription factor doesn't fluctuate much from cell to cell, then the pink gene will also not fluctuate much from cell to cell, whereas in this condition some other transcription factor that is regulating the yellow gene may be much more variable in its activity from cell to cell, then the yellow promoter will also be more variable in its expression from cell to cell so that this noise in these regulators propagates to the targets, right, and so which genes are noisy in a given condition is basically determined by which regulators are noisy in a given condition and this varies from condition to condition. But the more regulatory inputs a gene has, the more likely it is that at least one of these transcription factors is noisy in this condition. So in general it will be that the most noisy promoters tend to be the ones with more regulatory inputs. Okay, so these observations are explained by this idea and we sort of also tested it a bit more directly by using this embarrassingly simple model where we say let's try to explain the noise of a given promoter in a given condition by a linear function of how many binding sites this promoter has for a certain transcription factor T times some noise propagating activity of the transcription factor T in condition C. So this is the simple linear model. So this thing is measured, this thing we know from the literature which promoters are targeted by which transcription factors. So we can now fit these noise propagating activities to try and explain the variation in noise levels and we see that we can, it's an incredibly trivial model so it only explains a modest amount of the variation in noise levels across genes in each condition but much more than when you randomize these things. So this simple model that the noise of a gene can be explained by the noise of its regulators can capture a substantial amount of the variation in noise levels in each condition. All right, so that was point two. Gene expression fluctuations come from propagation of noise through the regulatory network. Ingredient three, phenotypic heterogeneity systematically decreases with growth rate, okay? So we looked at these noise levels and now you can ask how do these noise levels depend on the growth rates of the cells? And then basically what we see is that both this lower bound on noise, so this is this noise floor, right? This is the lowest noise level that unregulated promoters have, systematically decreases with the growth rate of the cells and then also if you now look at the distribution of this excess noise, this noise on top of this lower bound, this is much, has a lower mean and a much narrower distribution in fast growth than here in stationary phase. So as you grow slower, both the mean excess noise and the variation in excess noise across promoters gets bigger, all right? So the general observation is when cells are growing fast, there's also much less noise and when cells are growing slow or our growth are arrested, there's much more variability in noise levels and we think, although we have not yet, okay, so this may be true, but I'm still not entirely sure that this is the main reason, but it's sort of, it's logical to suspect that maybe the same mechanism as that I told you about earlier for these regulatory switches is at work here that when cells are diluting faster, that fluctuations may be dampened out more effectively than when cells are growing slow. All right, and so the final ingredient to this little picture is something that Don talked about last week already, but I don't know the overlap of the number of people is, let's say, modest, so I will very briefly mention it again and that is that a strategy in which cells randomly switch their phenotype at rates that decrease with the growth rate of the cell can be a very efficient adaptation strategy. All right, so many of you have probably heard of this idea of bed hatching, so I'm showing here a paper from Edo Kossel and Stan Leibler from 2005, where the idea is that single cells sort of stochastically switch between different phenotypes and then environments also stochastically switch between different environments and the idea is that, so environments, they randomly switch, cells also randomly switch phenotype and you can describe this kind of system by what is the growth rate of each phenotype J in each environment I and what are the switching rates that cells have from each phenotype J to I, which you assume is independent of the environment, right, because otherwise they would be sensing their environment, so this is really stochastic switching that has nothing to do with the environment you're in, you're just randomly switching yourself in between environments and then you can in such a model work out long-term evolutionary growth rate and see that such a bed hatching strategy, where there is no sensing or regulation at all, can still function well as long as environments are long lived enough and as long as the number of different environments you switch between is not large enough, so basically what you see here in this very toy example is the cells they start out in this purple environment and there are three phenotypes, purple, red and green and in the purple environment only the purple cells are growing fast but they randomly switch between, so what has happened when they start out in the green state, so all the cells are in the green state and only a few in the purple and red, but now in the purple environment because the purple cells are growing and the red and green are not, they start taking over the population and eventually they dominate the population and so if the environment lasts a long time you have a good growth rate, now the environment switches to the red environment and then you see well there were a little amount of red originally but they expand and then after some time now again the population is dominated by red guys and so you can work out that the long term growth rate that you have with such a bad hedging strategy is the maximal growth rate minus a cost that goes like one over the average length of the environments that comes from the small amount of other guys that always exist in each environment plus another cost that is coming essentially from the entropy of the environment that you don't know between which environments you're going to switch. All right so this was the sort of standard bad hedging model and so but now what Don did is he said what if I add one more ingredient and that is that even though the cells are not sensing their environment, they're sensing their own growth rate and a fast growing cell is just less stochastic than a slow growing cell so the switching rates are systematically higher for slow growing cells than for fast growing cells and this is the only ingredient that you add and now you see that basically that adds one more term here in this equation and this term can be very large depending on what is the rates of switching between fast and slow growing cells and basically the idea is when the environments changes now all these cells they were growing nice and fast they find themselves in a new environment they stop growing fast, they're growing slow and they essentially panic they become very they become much more heterogeneous so they're all starting to change their phenotypes until some guys happen to venture on a phenotype that supports growth in this environment and when they start growing faster they also automatically stabilize their phenotype. So the fact that they not only grow more so they expand but they also stabilize their phenotype whereas the ones that still haven't found a good phenotype keep being very fidgety and changing their phenotype this usually improves the effectivity of bad hatching. What's the time now? Ah, okay, so now I will tell you this thing. Okay, so all of you know, yes. So this is really beautiful work in terms of the four points that you mentioned I think only in point one there is sensing, right? In all of the other points it's only regulators that are present and that at low growth rates produce more different phenotypes and then this can lead to adaptation. So can you speculate a bit on the generality of this? So basically does this only work for cells that have lots of regulatory programs and cells that have few regulators for example cells with smaller genomes it wouldn't work for them? Well, it would work but it would work a lot less because they have a lot less phenotypic dimensions to explore essentially. And do you think there's a large cost to carrying a lot of regulatory programs? No comment, all these things of this is costly not costly I have no idea. There's so many cases where there are things where we obviously think in the lab this is gonna be costly and then we cannot detect any cost. Okay, so yes I can sort of speculate but I think all the speculation is kind of pointless. I don't believe we know. We have no idea what they're trying to do. I have no idea what these cells are trying to optimize, zero idea. You showed this plot in the beginning where you know lower, smaller genome size means fewer transcription factors, right? Yeah, the number of transcription factors goes quadratically with genome size, yes. So these cells would have a harder time to adapt? Well, it is very, okay, so if you go all the way on the cell, Michael Plasma genitalium, right? Has 400 whatever something genes. It has like one, two transcription factors depending on how you count, right? Because is the RNA polymerase a transcription factor? Well, yeah, of course it has that. It has a sigma factor, maybe it has one heat shock or something like this and then it's game over, right? If you go to Streptomyces chalicolor which has 10,000 genes, it has 1,200 transcription factors. They had more than fly, fly has 800, okay? So yes, the regulatory complexity is going up really, really fast, right? So again, I've been talking for 20 years about why is that? And we have some ideas, I mean, Sarah had some very good ideas of why this is happening, but I would say, okay, is it really totally convincingly show understood why and what is driving cells towards higher number of transcription factors? I don't think so. But this is a totally different topic, I would say, right? I'm just asking, how is E. coli getting to grow in heavy water? What is it? How does that work? How did it solve the problem? Yes. Hi, Eric, nice work and nice addition to the good old Leibler-Cassell model. And I generally, I buy what you're selling. I have one concern though, that looking for adaptation to something completely new, I just don't believe that you can do it by pure, shooting in the dark with all the noise firing and all from all cannons. There should be, again, the fact that the noise increases as the growth rate slows down is real and it helps. But I believe that there needs to be yet another ingredient to this model. I kind of only have a vague idea of how it should look like, but you should be looking for this adapted solution hierarchically. You first kind of start by adapting expression level of all genes kind of systematically by, for instance, changing the level of super coiling or something. And that gives you kind of a rough adaptation to a condition and then you start fine tuning and you kind of fine tune because if you are just, there are so many combinatorially many things which you need to optimize that by just doing it, by having everything noisy, would not solve the really complex problems. That's kind of my gut feeling about it. And again, I have only one data point which is not exactly the adaptation, but rather evolution, but you may say that adaptation is just a fast evolution. So when you look at what mutated first in Lensky experiments, one of the earliest mutations in pretty much all of the lines and which happened to be also is the largest fitness increase was some protein controlling the super coiling of DNA which is like controlling the expression levels off across the entire genome. And then you can kind of then start fine tuning, maybe you overshoot here and maybe undershoot in here and then start kind of fine tuning. So that's kind of my gut feeling about the very complex problem of looking for an adaptive solution. Okay, so I think we have to make a decision whether we talk about this during the coffee break or I'm trying because I mean, I think I agree with 80% of what you say and I have a lot of stuff to say about it, but it's all kind of speculative. So it seems to, okay. So we could go into discussion now or I could try to get a couple more things out. I don't know how much. Because otherwise this discussion is sort of open-ended I think. So, and I realize I should have taken you through this because so this is my sort of speculative picture of how I see this working. It doesn't it doesn't yet contain all the ingredients that you also touched on, but this is another thing and I don't want to discuss this now. So, all right. So, okay. So in this picture, in this cartoon here, this three dimensional space is phenotype space. Okay, so phenotype space is way higher dimension but here it's three and then each dot is a cell and then the color tells you what is the growth rate in different parts of the phenotype space. Okay, so here this bull's eye here, that's where the growth rate is highest then it goes down here. There is another patch here where the growth rate is also reasonable but not as high as here. And then there is a larger area where there is some growth but it's not so bad and then outside there is no growth, right? And so, so the sensing and regulation do not basically set one phenotype for the cells but they restrict cells to some subtype, subspace of phenotype space that based on the sensing cells know this is roughly the area where I have to play. Okay, so certain things that you know are certainly not there, they're often certain things stresses that are certainly there you respond to and so on but it leaves a large space of things that you're not certain about and those regulators will be fluctuating from cell to cell because they're not quite really sure about the environment and that those fluctuations will propagate and cause these cells to sort of randomly move through this subspace that the regulators have constrained sensing and regulation have constrained them to but the movement of subspace is not really random, right? Because it's still controlled by fluctuations that they sense propagating through the regulatory network and turning genes up and down that are relevant for the regulators that are fluctuating, right? So it's not a totally random movement. Then the growth rate sets the sensitivity of the regulatory circuits and the rates at which the cells move. So that means that if you're in an area of the space where the growth rate is lower you're more likely to move than if you're in an area of the space where the growth rate is faster. So the arrows are bigger here than they are there, okay? And this now causes because also these cells because the cells that are near these high growth rates not only slow down their diffusion but also increase the rate but they're also duplicating it at a faster rate. Not, but it doesn't take much time before most of the population is found in the region of the space where the growth rate is best. Okay, so that's sort of the picture that I wanted to and so, okay, so either we can now discuss or I have five minutes in which I tell you about how this is used to determine the sugar carbon source hierarchy in E. coli. Okay, so as all of you know or the rate at which E. coli can grow on a given carbon source is a hyperbolic function of the concentration of this carbon source. So the growth rate is called the monocurve as a function of the concentration is something like this. Now imagine cells are growing at some rate and some new nutrient X appears in the environment at some concentration C. Now the cells are gonna have to decide whether they're gonna switch to eat that nutrient or they stay with the nutrient that they're currently eating and the growth rate that they can achieve on X is a hyperbolic function of this concentration C so it follows a curve like that and so if your current growth rate is this purple growth rate here then essentially you will only want to switch if you're gonna improve your growth rate so that says there is some critical concentration here. I would like to only switch if the concentration of the new nutrient X is bigger than wherever this current growth rate intersects this monocurve, okay? So that basically says I want the critical concentration of this nutrient X to depend on the current growth rate that I have in a way that is the exact inverse of this monocurve, all right? So depending on how fast I'm currently growing I'm going to switch to X but I'm only gonna switch to X if there is more of X namely sufficiently more that I will grow faster when I've switched, right? And in order for that to be the case this induction threshold has to grow with growth rate as the inverse of the monocurve for that nutrient. Okay, so we've just seen that due to this growth coupled sensitivity, right? These feedback loops only go critical at the rate that depends on growth rate and it goes up with growth rate and we saw that it goes like lambda squared divided by the expression of the promoter, the production from the promoter as a function of growth rate. So now the question is can I pick that function, right? So this is what is the full induction of the lack operon as a function of growth rate? Can I pick that in such a way that this function becomes equal to that function, okay? So the question is, can we pick A of lambda such that secret as a function of lambda is the C-mono? So this is the monocurve. This is the one that came from this growth coupled sensitivity. I want them to be equal, okay? So these things need to be equal. That says the production from the promoter has to go like growth rate times one minus growth rate over the maximal growth rate as a function in this carbon source at saturation. And that's equivalent to saying that the full induction of the lack operon as a function of growth rate must decrease linearly with growth rate, okay? That's what comes out, that's what you have to have. It turns out we already know from work from Terry Wa's lab that that's exactly how CRP regulates the lack operon, okay? It's going on linearly with growth rate and it intersects at the maximum. And so this says CRP regulation already implements this, okay? So then we can go test this. So we tested this in the mother machine. So these were some heroic experiments that were done by Tomain and Theo actually also where we basically grow E. coli with this Loxy GFP in the mother machine, either in just lactose or just glucose at different concentration of glucose going down to very low levels or a mixture of lactose at a fixed high level plus glucose at different levels, right? So here this is the theoretical prediction, right? So now the critical concentration is exactly this inverse of the Mono curve. And the first thing that Theo and Tomar checked is that it's indeed true that as I'm lowering the growth rate by lowering the concentration of sugar, the Loxy GFP at full induction is, so with growth rate, it's going down linearly, right? So this is now measured at the single cell level. So this confirms the results previously from the while lab in the bulk level. But now we can go to the single cell level. Okay, so what do you see here? So here on the left, this little pink dot is showing you what's the distribution of growth rates of the cell when they grow only in lactose and then all the cells are induced. In light blue, you see the distributions of growth rates of cells when they're growing only in glucose of different concentrations. So you see that that is essentially following this Mono curve where this is the maximal growth rate and then it's below sort of 20 micromolar glucose that starts going down roughly linearly. And now the dark dots are when the cells are growing on a mixture of lactose and glucose at different concentrations and then we can look at the cells and we can see from GFP which individual single cells are induced and which individual single cells are not induced and then we can compare what are the growth rates of the cells that are induced with what are the growth rates of the cells that are not induced and we can ask what fraction of the cells is induced. And here you see what is the fraction of cells that is induced as a function of concentration of glucose and you see that if the glucose concentration is low everybody's induced and then at some point it switches over and now nobody's induced or almost nobody. And so what you see here is that when you're at very low glucose, the growth rate on glucose is much lower than on lactose and essentially everybody is induced and at some point here there is this switch and the switch occurs exactly when the growth rates of glucose and lactose are matched. So we indeed see that this system when you change the amount of glucose by the time you added enough glucose that the growth rate on glucose is now equal to the growth rate on lactose now the cells start switching. So the cells indeed implement this and then finally for you guys know about these growth laws, right? I can also change growth rate by adding chloramphenicol by slowing down translation, right? And as you may have seen, then if you ask what is now the expression of the lacquer poron as a function of growth rate is not going down linearly it's going up linearly with growth rate, okay? The P sector is now going up linearly with growth rate not down linearly with growth rate. We also confirm that, okay? So this is in the experience we did we see also that the maximum Loxy expression is now going up linearly with growth rate if you modulate growth rate with chloramphenicol and then the prediction of the theory is that the critical concentration should now be independent but because instead of going like one over lambda it's going like lambda and it cancels the lambda squared and then we confirm this as well, okay? So when you modulate the growth rate not with nutrients but with chloramphenicol then the cells don't change their sensitivity. Okay, I think that's it. Yes, that's all I wanted to tell you so that's done. I thought we have time for a couple of questions and then we can move to the coffee break for the discussion. Thanks, nice stuff. So I was wondering, you showed this connection of promoter noise and the number of regulators. Can you comment on the role of binding side affinity in this whole story? It needs to be high enough. I don't know, can you make the question more concrete? Obviously the amount of binding is gonna depend on the binding side affinity but it depends a lot on other things. Where is the site in the promoter? Sure, so I'm wondering if there's also a connection of noise to binding side affinity for different transcription factors. So how noise then is integrated again? Okay, what I can say is that we've tried to understand sort of can we get a better biophysical understanding of how noise propagation works for let's say one example, Regulon. So there's one example Regulon, the Lex A Regulon where we looked at promoters that are only regulated by Lex A as far as we know but have sites of different affinity or different numbers of sites and then basically put the cells in a condition where Lex A is a bit induced because there are some double strand breaks but not so much that they die, right? And then see how's the noise of these promoters going as I make more double strand breaks or less double strand breaks. And it turns out to be very complicated, okay? But all I can tell you is that yes, depending on precisely what kind of binding sites you have where, how much noise propagation you're gonna get at what level of fluctuations in the regulator may be some non-trivial function, okay? So there's no simple rule as far as I know. Thank you. Thank you, Eric. Have you looked into DNA methylation which is a long-term way to fine tune gene expression? Not in bacteria as far as I know. I mean, maybe I'm unaware but this is in eukaryotes. In bacteria, DNA is mainly used for repair to know what is the new one, what's the old strand as far as I know but I don't think it affects gene regulation. Okay, in biology, everything never, okay. Sure, there's some effect. But I don't think it's like in eukaryotes that it's a main tumor of gene regulation. In eukaryotes, the old story with nucleosomes and chromatin becomes a totally different question of what determines noise levels. So, yes. I mean, just related to the first question. So is there any relation between this noise level and codon bias or as anyone, but? The codon bias is in the open reading frames where the binding sites are in the intergenic regions so they're sort of in different parts of the genome. There's no codon bias in the intergenic region. Okay. Thanks for the talk. I was thinking about trying to like see the generality of the model in the sense that maybe grow rays is just one of the control parameter we can use maybe for other kind of organism that are not necessarily always fast growing, something like that in ecology, we have many niches. You can implement something very similar in the sense that something else is regulating the sensibility of the cell. Like, I don't know precisely, but it is like the control parameter can also be a parameter of your general framework. Maybe not only grow ray, maybe if you extended to teach us on something like that. I mean, you can imagine using any signal to set the sensitivity of your regulatory circuits in one way or another. The question is you get this one for free because it's done by delusion. You don't need to have any machinery to do it. And the second is the growth rate is really a thing that tells you whether you're doing well or whether you're doing badly, right? Because I really don't know what is fitness, but in general, when you grow faster and more in the same environment, you're doing better than when you're not. Generally, right? So this parameter, it's not just one random phenotype, right, it's phenotype. I was thinking about the regulation in general in the sense of a tissue, for instance, that are heavily regulated by well-defined signals, like growth factors and so on. Maybe you can extend that the growth factor have some kind of similar effect on the sensitivity of the whole network. And that's how the network, like the same way it will pursue or modify their phenotype searching so to feed growth rate in this case, maybe in the tissue they are trying to feed this other, let's say, artificial environmental signal that is the growth factor. It is certainly true and I certainly like to speculate that the sort of sense that you can have a regulatory switch turn on or off dependent on the growth rate of the cells may also be used in development to make certain cells switch to certain fates where other cells don't switch to certain fates. So there might be a distribution of growth rates in some precursor tissue where cells are differentiating such that now the faster growing guys in this tissue are gonna go to one fate and the slower growing guys in the tissue are gonna go to another fate and that can be used in development, this mechanism too. Yes, I'd like to speculate that this happened. I found a way how to turn my kind of very nebulous comment into a sharp question. Is there, based on your theory, regulator, noise and regulators is one way how the cell searches for new phenotypes and we know that regulators come in different out-degree distribution. Some are global regulators controlling many things, some are very local regulators. Do you see any trends in the noise level of a regulator as a function of its out-degree? You have convincingly demonstrated that the larger is the in-degree of a gene, the higher would be the noise just because there are more independent regulators. What about the out-degree trend? It depends on the condition. That's the problem, right? So that there are some conditions where the lack of put on becomes very, very noisy, right? And even though it targets only one thing, most conditions it won't be noisy, right? And so, and there are also some conditions where, CRP is so saturated, doesn't matter that it targets so many things, it's not gonna propagate any noise because it's not noisy. So it's really a condition-dependent thing. I mean, the only thing that, so we've asked are there any regulators that are always propagating noise, no matter what, in the eight conditions we tested. And then we found this is mainly those, those histone-like things, like this HNS, PHIS, IHF, those things, if you have predicted binding sites, that seems to predict that you're generically more noisy across all these conditions. And they're global regulators. They are global regulators, yes. But for many of the ones that listen to signals, right, there it looks like it really depends on whether the signal is in a regime where they don't really know whether to go on or off and some go on and some go off, right? At some point you showed a formula, you derived it from some circuit about the induction threshold as a function of the growth rate. And did you mention that there can be many circuits that will achieve the same thing? Is that a fairly robust thing, that quadratic dependence that you've got? No, no, no, you can change the scaling. But this circuit is, I mean, this thing is if any circuit has been studied to death, it's this one, okay? So the luck circuit, I can tell you about it. I found out trying to search the literature going all the way back to the sixties. But there, it's not like we're guessing this circuit. This circuit is very well understood. Yes, but you know this, you had a formula where the induction threshold was quadratic in lambda and it had that denominator A of lambda. Yeah. Which you mentioned at that point was a slowly varying function of lambda. But as it turns out later on, it's a linear function. Wait, wait, wait. Now I'm confused. I'm confused about your question, but there it is. Yeah, so you had that, right? Induction threshold, that A of lambda, that's the quadratic function on top. And this A of lambda is a slowly varying function. These two you can ignore. Okay. Unless lambda gets very, very small, okay? Go growth or rest, then these things matter. But if you're, okay. A of lambda goes like lambda, one minus lambda over lambda star, where lambda star is the maximal possible rate you can grow on any carbon source, okay? And the fact that it goes like that is because of the way that CRP regulates this operon. But I can change this. I can make this a constant, right? I mean, this is a function of what the promoter is regulated by. And I know that this luck operon is regulated apart from the repressor that is in this circuit by this global regulator called CRP that is basically sensing how good is my CRP, my carbon source? And what is the carbon flux? So I just wanted to ask that this quadratic dependence on lambda, is it very generic? Yeah, but this comes from the fact that there is one dilution rate of the intracellular inducer. So the concentration of the inducer is basically a balance between how fast is it pumped in versus how fast is the cell diluting. And the level of this luck C and luck Y, they are a balance of how fast that are the proteins being produced by gene expression and how fast is dilution diluting them out. And these two factors, lambda, give you lambda squared. But like in this two component system, I can easily make a lambda to the third if I want, okay? Because there's an extra lambda in there. Okay, okay, we gotta go for coffee. But thanks for the patience and thanks for the talk. I wanna just circle back to the deuterium and the kinetic isotope effects. Yeah. So we've got this dilution going on, changing the concentration of molecules. That's setting the sensitivity. We've got this regulator target relationship going on. But I can't connect this to deuterium because it seems different. When you swamp the cell with deuterium, there's no escape from it. So you can't dilute your way out. And so it just seems like a little bit of a different problem or a concept in my mind. And I'm just, I just wanted to have a little bit of a comment or explanation about how you see the relationship between the KIE and the metabolism. Okay, so you wanted to waffle less and be a bit more concrete about how can this possibly solve this deuterium case, right? Everything you presented was good and not waffling, but I'm lingering with the KIE. No, but no, okay. So I think this also comes back to something of Sergei that I haven't answered yet, but I'm not gonna answer now. But the thing is, so what I'm imagining is that the cell has sort of internal, the sensors that are there are not just for the outside world, but it's for how am I doing myself? Okay, and so when a certain flux is too low, right? Because you're using up these components faster than they're coming in. This may now activate whatever the upstream reactions are that typically increase that flux, right? Because so the cell has a logic to say to that certain things are not going fast enough, certain things are going faster. So what I'm imagining is when you add to deuterium, certain things are now going way faster than before, certain things are really slowed down, and basically the cells are sort of randomly trying out changes until they hit on something where these fluxes are working better than they were before. And so this is also the way you see the state, you see that certain reactions that now run much faster, slower with deuterium than with normal water, some dehydrogenation or hydrogenation reactions. These enzymes are totally upregulated. They're way more of them than they are normally. But I think that it finds its way to such a solution largely by trial and error. Very last question. Yeah, it's kind of similar to Sanjay's question. So for growth rate dependent sensitivity, you say that it's mainly mediated by dilution. Of course, that function there, it's also seems pretty important, right? So in some sense, growth rate dependent sensitivity is affected by dilution, but there's also another component, right? Which is basically how these parameters depend with lambda. And... Which one? So the A parameter, for instance, right? So just to see if I got that right. So for a constitutive promoter. Yeah, exactly. A is essentially roughly constant. Not quite true, but okay. For the lack operon, we know that it's going down linearly with growth rate because of the COP thing. But if you're changing the growth rate with chromophonical, we know it goes up. And actually it will precisely compensate the lambda squared when you... So yes, I totally agree with you. But generically, there will, like if you have two intermediate steps, there will be a lambda squared that you have to compensate. And if you don't, if you have a constitutive expression, then it will go roughly like lambda squared. So it's sort of the default case is that it will become less sensitive, but of course you can regulate your promoter to counteract it. Of course you can do that. Okay, let's thank Eric again. And the scores per tradition, we are late.