 All right, this is going to go wrong. So I'm going to give an answer to this question. How do microbes adapt to different environments? And the answer that I'm going to give is somewhere in between a fantasy, a proposal, and a theory. So this should give rise to lots of discussion. I would be happy to hear your opinion. So first, introducing the question. Microbes can adapt to many different environments, of course. We all know this. And often the environment is not known. In the future, in the wild, many things can happen. You can have nutrient changes, antibiotics, salinity, temperature. And somehow these microbes can still adapt. And for example, if we look at our favorite E. coli, we can grow it in the modern machine, as they do in our lab. They can grow in the gut, and they can grow in wastewater plants. It's quite a diverse spectrum already. But even more striking is that if you give them something that they've clearly never seen before, even to that they can adapt. So this is a study where they took the growth medium and took all the hydrogen atoms from the water and replaced it by deuterium. And E. coli just completely reshapes its proteome, all the, well, everything changes. And still, they can then grow again. So well, one theory that people would like to give, it's a bit extreme how I presented, is that, well, microbes have just learned by evolution to set the right phenotype in all these environments. So sensors have evolved such that they can know in what environment they are. And then they have regulators that know what phenotype fits this environment, and that is how it goes. But this is clearly wrong. So how can you have learned what you never saw, as in the case with the deuterium? So evolution cannot have shaped you to address that. At the same time, how can you be precise? Well, we know that gene expression is very noisy. So even if you know what you have to do and you want to do that, gene expression is so noisy that you might just do a very bad approximation of that. And then last, there's, because given the small molecule numbers in cells of transporters and sensors, we know that there's just fundamental physical limits to how much information you can gather about your environment. So it's impossible to know exactly the glucose concentration in your environment. So I propose a different hypothesis, or well, an open hypothesis. I just say microbes must use some trick that makes this phenotype search easier. And my talk is about giving you a trick that I think is convincing. So this frame, hopefully, will be filled at the end of the talk. So let's take a very simple model system. We just have three phenotypes. And in a purple or red and a green one, and then in the purple environment, as indicated by the background of the square, only the purple one grows. Then over time, of course, the environment can change and we go to a red environment, now only the red phenotype can change. It's still quite easy. But now we have to come up with some model, how the cell is going to adapt and find the right phenotype. And when I started thinking about this in my PhD, I was heavily influenced by this paper by Eric van Inwege, which is why I'm now in his lab doing my postdoc. It's important, well, it shows that expression noise, which I just proposed as a nuisance to gene expression, can really help in adaptation. And this is also apparent in a famous paper by Kossel and Leipler, where they show that bed hedging can help a population adapt. So I'm going to go extend this last paper a bit. So let's first recap what they do. So I extend this model, whereas these three phenotypes, with random switching rates between these phenotypes. So these are indicated by the arrows in between the circles. Cells can just randomly sometimes switch from phenotype to phenotype. And what does this do to your adaptation? Sorry, one point, what I'm going to show you is that even though the single cells do not have a bias versus going to the right phenotype because they're switching all the phenotypes at the same rate, they will still adapt on the population level. Well, how come? Because if you start in an environment, each cell will randomly search through the space of phenotypes. And so starting in the purple environment with all cells in the green phenotype, they will just randomly switch sometimes and they might happen to be in the purple phenotype, which will then start growing and will outgrow the rest. So we just have some phenotypic selection here. If you go to the red phenotype, you see that the red environment, the red phenotype, takes over. So Gosson Leibler made a nice model and it was already quite simple, but not simple enough for what I'm going to do after. So I'm making my simplest model of this system. So I have one growing phenotype, the purple one, and there's N non-adapted phenotypes. And I say there's only two growth rates, a fast growth rate and a slow growth rate. And because I can scale and shift, these growth rates are going to be one and zero, but that doesn't matter. Then I choose a fixed environment duration because I just want one parameter that says how frequently I shift. And this environment duration is called T. Between the phenotypes there's constant switching rate, phi. So this gives rise to some ordinary differential equations where I can kind of group all the non-adapted phenotypes into one group because they have the same dynamics anyhow. And so this is sort of SB. So it's bad, B is for bad. And the SG, so the good phenotypes. You see, well, it makes sense, right? So they are growing with a rate of one minus the rate at which they're switching to other phenotypes, phi. But there's also cells that were non-adapted that switch to the adapted phenotype. But only one in N times, this is the right switch, because there's many options to do a wrong switch. So this is the growth in the environment. Then if we go to a new environment, there's a certain, before you switch, there's a certain fraction of cells that are adapted. And this is this P, or P at the time point, T, which is the time point of switching. Now I'm going to assume that the cells are equally distributed over the non-adapted phenotype because it's just equilibrated. It comes down to some mild assumptions on the length of the environment. Then I can say that the new starting fraction in the new environment is one over N times the number of non-adapted the other fraction of non-adapted cells in the previous environments. Because all these cells that were non-adapted have a chance to be adapted to the next environment. So I can solve this model. And I can then look at the long-term growth rate. With the long-term growth rate, I mean, just the average exponential growth rate if I take the number of cells I did. End point divided by the number of cells at the begin point. Now I just want to make clear that this is not a phenotype. So there were some discussions that I think are sometimes a bit confusing because we don't use the same wording. So when I talk about this long-term growth rate, this is the average growth rate. And there's no discussion about if you're selection for this because this is the definition of being selected. It's saying how many does my number increase. I agree that the growth rate in a certain environment or the maximal growth rate, this is a phenotype, but this thing what I'm going to maximize, this is just evolutionarily selected. Having that out of the way, I can now just use G. And I find that if I optimize the optimal switching, the switching rates, and of course I don't know that this thing is optimized. And I can show you plots later where we don't do this and we get, well, similar results. So I can show you at the end if you want. But if we optimize this, it's already interesting what comes out because the optimal switching rate turns out to be one over T, one of the environment duration. And Kosovo and Leipzig already found this, so this is not mine, so I can say that this is a very nice result. I'm not bragging. But this has a deep relation with optimal portfolio theory or betting on horse races. You want to bet on the strategy in proportion to the probability that this strategy is going to be successful. And this one over T is the probability that you're going to switch environment. So that's why this comes out. And then the long-term growth rate is also a beautiful formula. It has just a maximum growth rate you could possibly have, one as an upper limit, and then two cost terms. So you have a diversity cost, which is the cost of switching to different phenotypes at one moment. And then you have a delay cost, which is after every environment, you need some time to expand the pre-adapted sub-population to take over the population. Yes. Yeah, just a curiosity. I mean, it looks like it's not a dimensional what you have in the log. So there should be another time constant. Ah. Ah. That I would have to look up. There are some rescalings that we did because phi is divided by the growth rate. So I think that's why it's undimensional because we rescaled it by the maximum growth rate. But yeah, it's a good point, but I might come back to it. Yeah. So if we see what the results are for if I, well, my model is really simple, right? I have only two parameters. I have an N, which is a number of non-adapted phenotypes, which kind of captures the how hard my search problem is in phenotype space. And I have a T, which is how long my environment takes. And now you see that you can go even without any regulation, without any bias between which phenotype you switch to and not, you see that you can get to reasonable, reasonably high growth rates, average growth rates, if you have either a small number of phenotypes, so it's a relatively simple problem, or you have a long environment duration. So this is indeed what the Kassel and Leipler found. Bet hatching can be effective, but only if environments are not too diverse and environments change relatively infrequently. Now, this was showing that bet hatching could work, but it would have also put bet hatching for a very long time in a sort of corner where it could only solve relatively easy problems. So antibiotic persistence, this is generally accepted to be that you can solve this with just switching sometimes to a persistent phenotype and because it's only two states, right? You are either persist or not. But in the wild, just changing, adapting to all kinds of different environments, different nutrients, different everything, and this couldn't happen very frequently. It was not thought about that bet hatching could do this. But I'm going to give some experimental observations that make me think that it is actually possible to do random adaptation to quite a good level. So this is work done by Thomas Joulou and Theo Javert, who is also here in the room, on the LAC operon. And it shows that regulatory switches become more sensitive at low growth rate. So let me first quickly introduce the LAC operon. So it's needed to do the uptake of lactose. And it has an inhibitor, LAC-I. So to judge that if this is repressing the operon and if there's then lactose outside the cell, or in this case, inducer, because this is artificial inducer, because they do the experiments with that, it cannot take it up. But sometimes there is a bit of leaky expression of the transporter. This will make sure that the inducer is imported. The inhibitor is inhibited and you will kickstart the system and LAC will be fully turned on. So you can look at this switch in different conditions and ask how much artificial inducer do I need to kickstart this operon? Now you can see that the critical concentration of inducer that you need really shifts between conditions. And what is even stronger is when you plot this against growth rates, you really get a teri-wa-like plot, I would say. It's a beautiful straight line. And what you see is that cells become more sensitive to fluctuations, these small or outside concentrations, at low growth rates. So this is something I will take in the next part of the story. Another thing is that we also saw that growth rates lowers the gene expression noise. So this is looking at high-copy number proteins and then at the noise floor, they will not go to zero in their noise, but it will, there also the noise floor will decrease with increasing growth rate. So together with that, the gene regulatory systems can become more sensitive at low growth rates. Yes, low growth rates. Also the fluctuations in gene expression will increase, which just paints a picture that cells become more likely to switch between phenotypes. Now how do I put this in my model? I had this bed-haging model and now I can just change one thing. Whenever you're not growing, you're going to switch a bit more, which seems reasonable, giving the experimental observations that we have. But I will tell you that this is in fact the trick that makes life a lot easier for the microbes. So how does this work? Well, we have this system where we saw that bed-haging alone could make a population adapt, but now the picture drastically changes. If we introduce this growth rate-dependent stability, as we call it, the adaptation of the population to a new environment is much faster and it also goes to a higher, a final growth rate. How does this work? Well, if we look at the moment, at the point where we start a new environment, all the cells are in the purple phenotype. But when we switch to the red environment, these purple cells, they all start to stop growing and this will increase their phenotype switching rates. So these slow cells will kind of panic and just move around searching for a growth rate. And they will only stabilize once they find this fast-growth phenotype. And on top of that, so this biases already the population towards phenotypes where you grow fast. On top of that, they will still outgrow the other cells in different phenotypes. So you have a double advantage of being in this fast-growth phenotype. So I can, of course, also calculate the consequences in my model. Yes. Yes? Could you explain the reason for, like, there is a slight dip in the brown phenotype, even though there is a... I'm not sure. I'm not able to understand the graphs properly, I think. These are relative frequencies and they add up to 1. So there's no dip in the red phenotype, but there's just an increase in the green phenotype as well. Because the purple phenotype starts switching away to switch randomly to both red and green. So that's why you see the green increase and it seems like there's a dip in the red as well. But I don't think there is. Yes. So I change one parameter in my model to capture this effect. So only a multiplicative factor R that multiplies the switching rates from cells that are non-adapted. What are the consequences of that? Well, I pick a completely arbitrary R of 100. I don't know if this is reasonable. That's why I made it the parameter. Everyone can pick whatever they find reasonable. I just want to know, does it work for all these parameters? And what you see is that the growth rates for all parameters N and T increase and quite drastically. I can... Because I have such a small model, I can look at all the parameter combinations and you should read this that on the y-axis or on the x-axis, there's the strength of this growth rate dependence stability. So along the y-axis, we see the normal bed hedging. There's just a growth rate dependence stability that is one. So everything is the same. And if you then go to the right and on the y-axis, we change the parameters, the number of bad phenotypes and the parameter duration. And if you go to the right, you see that you always get an increase in the fitness. There are some more things that we can see in this plot. For example, what are these... They are going to aligns meaning where we can talk about this later. I don't have time. Looking at... Well, we try to, of course, do the analytical derivation and it's quite elegant. We just get the same expression as Cosmo and Leipzigot, including an extra term for the stability effect. And this effect can make this statement that we found from the Cosmo library paper change from bed hedging is only effective in such and such case to it can even be effective if environments are diverse and environments change frequently. It just depends on how strong your growth rate dependence stability is. So I think this is a really strong effect. So just quickly summarizing before I go to my last two slides, we found that bed hedging can make a microbial population adapt but only in very simple scenarios that were not really describing the nature in my view. But then adding the observations that cells become more sensitive and to fluctuations and get more fluctuations at low growth rates. This brings you to growth rate dependence ability and we saw that this can really make populations much more effective in adapting. But there's of course a problem. We should also at some point get out of our theoretical bubble and look a bit more are our predictions correct? Because if I say that all the switching can be done by just random switching then, well, why do microbes even have sensors? And we started thinking about this to say, well, we want one theory that incorporates both sensing and this randomness. I'll make an attempt here and this is where the fantasy part comes in a bit. So I would be happy to discuss it. If you have well here a metabolic network of course, well, I'm meaning all the genes in principle all the phenotypes are all the levels of genes that you can express. If you fluctuate randomly in this space you can have a very efficient search strategy but you're never going to find anything. It's just too big a space. So we need sensing and regulation. For example, we know that for the lacqueron that it doesn't turn on if there's no lactose. The genes are shut down and you don't have fluctuations in that direction. So what if we know in this network that these substrates are not around? Then sensing can limit the space that we have to search by just removing some reactions. They can limit the fluctuations there. Then on top of that there's a result also from the Lab of Erich van Inwegen gene expression noise is not random in all directions. It actually propagates through the gene regulatory network. What do I mean with that? That if there's a transcription factor that targets a set of genes that are often related if there's noise in the transcription factors it will propagate through all the genes. So I'm not just randomly fluctuating in all directions in the phenotype space but I'm having directed fluctuations which really limits the space I have to search because evolution has determined that these often correlate so I want to have fluctuations in that direction. If I have another transcription factor for a different set of reactions I can see that this will really help. I'm just adding the effective dimensionality of the phenotype space I'm searching. Together with the phenotype with the random switching rates and the adaptation that that causes I think this can go a very long way in explaining how microbes adapt to all these different environments. So I'm just adding these two last points to the summary and I'd like to thank Aachen who was my master's student and then we asked for a grant together to work on this it was a very nice year that we worked on this. Frank Bruggemann who is there on the bike and then the new group that I'm in of Erik van Inwegen and this band of noise busters that we are called. If you have time and you're interested we can also discuss this right picture after the talk because it's really there's so much to see. So I'll leave you with the summary and I'm happy to answer your questions. Thank you. It was a wonderful talk. I have one comment and one question slash comment. So first comment I see some analogy between this and the strategy in chemotaxes where you also the strategy is if you're doing well keep on doing what you're doing if you're not doing so well you randomly switch to other things that was the comment and the question slash comment is do you think that this strategy could be used for for optimization algorithms like a new type of evolutionary slash genetic algorithm or improving existing algorithms. So first we also thought about chemotaxes and Eric at some point told me I wouldn't touch chemotaxes with a 10 foot pole because this is the pet project of many physicists and there's been so much work but I do agree with you that there's a really good analogy. Yes so optimization that's also true Acha and I also looked at this at some point there's a very nice Wikipedia page of all the nature inspired optimization algorithm it's really impressive there's bees and every thing in nature has been transferred into an optimization algorithm I'm almost sure that if we try this there's already some other algorithm that does this So there's maybe something that I missed or maybe what I'm about to say is totally trivial but I think there should be a relationship between how fast you switch away from a phenotype and the growth rate of that phenotype I mean if you switch away these are two time scales you must be able to sense one of the two time scales before you decide to switch away No I don't understand it The switching rate should be slow enough for you to be able to quantify the growth rate where you are so I would expect that I agree completely for example when we looked at this plot there's some region that might not be so biological so if you go to very short environment durations here you can still get to optimal fitness which I thought is impossible but what happens is that you want your switching rate to go to infinity which is not it works because you will have a very strong bias between if you have a large enough R a very strong bias from switching to the fast phenotype versus away from it but I mean it's not it depends your growth rate before you can switch but you could of course couple not only to growth rate itself but also to flux in the glycolytic flux for example as in nutrient transport you induce a transporter when it doesn't start up you can immediately switch away again but I agree with you that there should be a cap on your switching rates but this is why R is also a parameter you can say this is no longer feasible actually a comment I think probably the cells can sense much faster that they are in a slow growth rate than we can see it takes much longer to see that the growth rate is low but I guess they sense it much faster than us somehow so my question was about your model of the switching is very discreet I guess it's like a set of N states and experimentally I think people at least believe that when you were starving for glucose they all the cells expressed all the transporters but I guess nobody really tested it in single cell level so do you think actually what we see is like an ensemble of different switchings that we think they are all doing the same thing so what I really believe is that you have some discreet part where you switch to the right pathway and then there is another optimization algorithm that within the pathway optimizes the relative concentrations now Bob will talk about this later but that is very deterministic what I did with Ache and this was the other branch of the project that didn't finish because my money was out and Ache had to go do his PhD somewhere which was actually saying well if you have a distribution on a continuous spectrum then it is known that you are also pulled towards the optimum even if you are mean in variance or you are mean of your distribution of phenotypes or concentrations that you aim for is different from the optimum you are pulled towards the optimum because there is just a selection of the cells that have the right concentration and they give this to their daughters and we wanted to see if this is also increasing if you have some growth rate dependent fluctuations but it is still an open question I think I also had a question about the switching rate so if cells get stuck in an intermediate going rate like if the phenotypes is not the best but slightly good and they become stable would they be stuck in there that's thank you I have an extra slide so in this model I made many assumptions I have a fixed environment time I have the number of environments equal to the number of phenotypes I have one phenotype growing the rest is growth arrested but of course I can sample all these things and what I did is I sample randomly growth rates I also said that the switching rates were optimized now I did all these parameters and I sampled them randomly as I could and I found that you always get an increase in your growth rate if you increase the strength of GRDS so to address this more specifically because I just wanted to put in this slide now to address this more specifically you still have a monotonic relation between switching rate and growth rate so if you get into an intermediate state you're still more likely to switch to the adapted phenotype than the other way around so you keep this bias but of course it gets less and less strong the closer your growth rate is to the optimal one but if you're already close to the optimal one it's also not so necessary to adapt so it's kind of nicely yeah I wanted to ask like according to this model how would you say this would then apply to that deuterium example you mentioned at the beginning and how would like a bacterium evolve a sensor to deuterium if it would or something like that I think in the deuterium the growth rate just drops a lot and they're just going to try out lots of different stuff and in the end they're panicking so much that some cell finds something that works sorry yes yes so sooner or later it finds a solution and it has to not die before that yeah I mean but if you consider like the space of possibilities is quite large so basically the cells would be trying everything at random that's like lottery yes well that's what I was pointing at at the end that there's of course some genes that are co-regulated and they fluctuate together so that you don't have to find to search the whole gene expression space so that's where sensing and regulation comes in I've also thought about can we somehow find the dimensionality of the search space but I really don't have a good idea of how to quantify this but if they do sense it then they cannot sense something which was unknown until then no that's not but they can regulate up and down the genes that are often that are needed together right if you have the whole glycolysis pathway and you're independently changing the genes then they cannot work but if you up and down regulate them together then they might work so if you expose them frequently they'll find a way to know that there's the uterium and they will then try to no I don't think so I just think they are changing around things until they find something that works on the you don't have to do it but I was asking then how would like a sensor evolve ah sorry I'm misunderstanding I haven't looked into this question that's a good question but no I don't know like what's your guess it really depends right on the nutrients it's often a transporter that already does a lot right so but the uterium I don't even know there's a question there and there yes but jocobo is telling me to cut it yes I think everybody with question has to just hoard around Dan and you'll have to answer to all of your questions over lunch okay thank you