 growth under high and low concentration of nutrients, so the next picket is used to swing Okay, maybe I need to bring it closer now getting very close here but Everything for the science now Okay, does this have a laser? Okay, no pointer Yeah Wow, okay. Thank you, Martina. This is sponsored by her the equipment. I Will list you in acknowledgments Okay, my name is Justus. I just finished my PhD in the group of Michael Monhard at ETH Zurich The group has now moved on to Rutgers University Michael is also recruiting so if anything that you see here is interesting to you and you're considering a postdoc in theory Then Yeah, please consider the lab. I'm Developing basically theory for the evolution of microbial growth traits Typical questions that I'm interested in is what traits should we expect from evolution and how fast do they evolve? The approach here is to understand selection pressures really well and really sort of in depth Using ecological models and then combine this with models from population genetics to come up with an evolutionary trend and The work that I'm going to present here came out at the beginning of the year together with our co-author Noel who is a postdoc in Zurich with Martin Ackerman and Together we looked at the evolution of growth at low concentration of nutrients and the background here is that microbes play a really important function in the environment one way to see this if you see these diagrams of nutrient cycles here different boxes indicate different forms that carbon is stored and say the ocean or land environment and you see these arrows and these are basically The fluxes I think in a year in the units of gigatons and microbes play a role in bringing down CO2 into the ocean and also then Leasing CO2 again when they eat say the marine snow and if you want to calculate any of these fluxes you need to know about the population growth rate of these populations and Growth is a complicated process inside the cell with many inputs. There is sometimes a Special scenario where we know that the entire process is limited by a single nutrient This is explicitly what you construct in a lab experiment with M9 where supply all the other essential nutrients a phosphine Nitrogen and high concentrations and then you know that usually glucose is the limiting nutrient and This is a nice setting because it sort of allows to describe the entire growth as the function of this one concentration And if you look for a function to describe this you end up with a mono model that was mentioned a lot in it in the talks before it's it's I think maybe the first law of quantitative microbiology And this is the curve that Monod described in 1942 in his PhD thesis and He used a relationship that was known from enzyme kinetics. It has two parameters a maximum growth rate That's the floor or the ceiling here and then this parameter K, which I call the half saturation concentration And it's sort of drawn in this Think line here the K has different Words sometimes people call it they're also the nutrient affinity or the monoconstant What's interesting about it? It's basically at the intrinsic scale of resource concentration for the organisms So this is a trait and it sort of encodes what? Concentration the organism needs to reach half its maximum growth rate When we think about the evolution of this trait It's relatively clear that lower would be better and in this model you can see if you lower the K You basically shift this curve a bit to the left and then you get higher growth, especially low concentrations So the intuition is clear But it's there's an opportunity to be more quantitative and we did basically two things we looked at an empirical distribution of these growth traits and Trade database we saw that there are systematic differences between species and That could be explained perhaps by evolution We'd also didn't see a trade-off between the K and the G max Or no evidence for it and then in the second part sort of used an evolutionary model to ask How should the K evolve now actually in numbers how much lower should it be and? It depends on the environment that you're involved in yes When you say trade database for G max and for K. Mm-hmm. I think now somebody mentioned that this this this K is all over the place, right? But what what empirical database yes, so it's a database we collected. It's a database we collected from literature data, so But can you make sense of it? I mean this case extremely difficult to measure. I think I think we can make sense of it I think maybe you let me explain a bit what we see and then the goal is also to sort of Resurrect the K measurements that it's not all noise, but there's actually some sort of signal in it and this is the starting point of this is the collection of these trade measurements and This is the work of Noel. She went out and looked for papers that basically took a species and Decided limiting nutrient and then measured this response and reported the K energy max. There were other Summaries of these data that we used One is from the from the 90s and the 80s these two modes we focus on systems biology organisms And then there's a lot of trade data from fighter plankton And the kind of table that we end up with is we have some information on the species on and their strain labels There are two trades G max and K and then we have sort of all these meta variables like temperature and experiment type Just to give you sort of a look At the historic trend this is the number of measurements that were reported in each year This is the original measurement of Mono, and then you can clearly see there's a trend 80s was probably the early 80s was probably the best time to Measure these these case and then people measure less and less and Two important things to say here that we took care to only include data from growth rate. There are other Limiting concentrations that are reported, but they're sometimes based on measurements of respiration or measurements of uptake When you check For In a subset of the data from this fighter plankton database You can see that while there is sort of a similar functional form for uptake Actually the half saturation concentrations are not the same we exclusively focus on the growth trades and We also have a lot of diversity of measurements in this data set. So there's say at least three ways to measure this You can use a chemostat and in the chemostat the parameter that you tune is the dilution rate And the parameter that you measure is the concentration at steady-state So if you set a range of constant dilution rates, you get this response curve You can also do this in a series of batch cultures where you tune the initial concentration And you always try to measure the growth rate at steady-state And then a third way is to do actually only one match cultural cycle and measure a time series And if you can sort of resolve the time points up here, there's some information on the K in this deceleration If you actually look into Monod's thesis, he used this large of the last approach There's some Fundamentally different biology going on. So this is a steady-state across environments This is sort of a trajectory where there's some sort of history dependence Both of them gave rise to the same response. I think this is something that at this point we only sort of accept But I think it would be maybe interesting from to hear from physical physiology people So all right the number three is especially even though it was a Monod original is especially a suspect here because If you are just about to finish the exponential growth you are transitioning to the growth You you may actually have your G max may change systematically because you start Preallocate and maybe resources for the next environment or for stationary phase And since all you can measure is a ratio between G max and K you you kind of rely on G max staying the same throughout the entire Entire growth curve That does make sense. I'm sorry. I didn't get it right now, but maybe we can well Yeah, we can we can talk about I think the question I want to ask is connected to this So you were saying that option number two and number three give the same response Do you mean that the values of G max and K that you get from these two type of experiments are the same? Something that we sort of explicitly checked But I I think I mean I didn't perform these measurements. I just wanted I think it's interesting that The mono model has been around for a long time They were always competing models that people proposed like the droop model and also a hauling type response But it sort of survived right? This is a model that survived 70 years and it was always sort of good enough for what the people trying to do and then apparently In both of these situations it fitted the data To the best that the original authors sort of could decide I'm going to move on To what the the data actually shows so this is our data set we have here a number of resources from left to right the most resource measurements are actually in phosphate and and as a sort of a Neutron that is much studied in marine organisms and then we have glucose is sort of a nutrient of systems biology You can sort of see it in the colors. So green are prokaryotes Orange are eukaryotes possibly cells a little bit larger and then we have different shapes for organisms that are safe auto trolls because they fix as fight as phytopunk than they fix energy from the light and classical hate or trolls like E. Coli and One thing to see here is that it goes 10 orders of magnitude If you consider all resources For comparisons so this dot here, it's at roughly 10 millimolar. This is a concentration You would use in a classical M9 medium with glucose. So that's your 0.2 percent glucose and Say the concentration that the LTE uses is about two orders of magnitude lower But it's still relatively high compared to these half saturation concentrations for E. Coli We see systematic differences sort of especially between phosphorus and the rest We don't really have a good idea why If you look at These dashed lines. This is another sort of sanity check. This is a concentration Where a cell with this volume one micrometer squared One micrometer cubic would have one molecule per cell so this is say roughly the volume of an E. Coli cell and At this concentration If you call I had a half saturation this low, it would be basically be able to grow at maximum rate with one molecule per cell Low most of our data points of E. Coli are actually up here in this glucose bar So it's a bit removed. So probably it's it's more like a hundred molecules per cell And then of course you have larger organisms Sort of this line goes down But it's sort of good good to see that most of these points are above the line There's two exceptions which are vitamins thymine and vitamin B12 Unfortunately, we only these are single measurements. We don't know about the variation in these but It would be highly interesting if somebody reports more vitamin measures in the future Sorry Do you have some data for the same organisms same conditions that we can see how many orders of active users between different data sets? I mean, I'm going to zoom in on glucose You mean Okay, so but these are not the same temperature or is there just like we're going to talk about temperature and experiment type Yes Yeah, you mentioned that you don't understand why phosphorus is the lowest But for instance There should be some correlation of this key with stoichiometry of the nutrient and Famously there is a Redfield law, which is approximate stoichiometry of carbon to nitrogen to phosphorus among marine organisms Which tells you that for instance nitrogen should be six times more Abundant inside the biomass and carbon is another hundred times more abundant than phosphorus So I would if I just squint at your data I will see that the carbon at least the glucose is Largest the nitrogen somewhere in the middle and the phosphorus is somewhere at the low end So that that may be the explanation for your trend between elements Yeah, I think this is this is exactly sort of the type of thinking Yeah, it would be very interesting Maybe we can build a model for it that connects these two things So if you zoom in on glucose you can resolve the variation by species and you see I'm gonna single out two species E. Coli and yeast and You can see Each of them has large variation, but there's still systematic differences between them there's next to no overlap between these two distributions and Systematic differences between species is also something that we see on other resources If we focus on E. Coli we can now ask okay where does all this variation come from and we have these meta variables that we recorded in our database and what I did I took This as the Predicting variable and asked how much of it can be explained if I correlated with maximum growth rate with temperature with the experiment type With sort of the strain labels that we have and then with the author So the author is a bit tricky I think the author is a combination of all of these two things So you have little publications that actually measure the same strains that other authors did so every author basically Came up with a Unique spot or a unique patch in this landscape of possible conditions, but they rarely sort of measure the same conditions that somebody else did Let's go The most I'm going the method is this experiment type That's where we record basically batch chemo start batch with time series and these things This is the next slide on this slide We had strain labels and Most of the strain labels were unique So there was only one measurement, but there was two strain labels that were where there multiple measurements One is ML 30. This is the original strain that one all measured and you can see it's different groups that measured it and They got Variation that was much less than what we see in the entire data set ML 30 or 8 is a mutant of ML 30 and here we see now Same strain with two very different values if you look at the experiment type now, so these experiments were either done in batch culture or the chemo start and These are all chemo starts measurement here's the difference between chemo southern batch so this is actually a paper I think that tried to explicitly test this and I think it gives us sort of an estimate like You can take this Basically, it could be off by 1.5 orders of magnitude or say two orders of magnitude depending chemo southern batch If you go to temperature temperature does not have a big effect. So these were actually measured at different temperatures And then maximum growth rate is actually uncorrelated in this data set So these are all the color measurements where we had maximum growth rate and you a trade-off here would be a positive correlation, but if you calculate the the rank correlation, there's No significant correlation at all This interesting this was interesting to us that there was no max correlation of maximum growth right here so we checked more closely we also see no mat correlation in the yeast and Then we checked on different nutrients and There's also the result is always the same when you calculate the rank correlation coefficient It's not significantly different from zero Okay, so what leaves this out with there's a large variation within species and we we see from like looking at an individual examples That maybe one or two orders of magnitude could be explained by the experiments for conservative But there's still systematic differences between species that are larger and This is not explained by selection on maximum growth rate So your maximum growth rate does not explain you okay, so this was interesting now because we We thought okay, maybe there's a history here that these strains say East and E. Coli have evolved in different environments in the past and that is sort of reflected in in their mean half saturation concentration this is a classic theme in Evolution that features of the environment imprint sort of on the organism. This is two birds from Darwin's finches Darwin's finches were studied I think first by Darwin himself who saw that they have different beak sizes and then later in 1950s by a Couple of evolutionary biologists and I think up to this day by Peter and Rosemary Grant and the idea One of the observations here is that the beak size reflects the size of the seeds that they're eating Something like this could be here in this microbes that E. Coli It's original habitat is the gut or say the waste water these are low glucose environments by yeast Is used a lot on fruits on and in baking conditions. That's a lot of sugar. So maybe that's reflected okay There's a hypothesis and we used basically modeling to test it This is the outcome of the modeling So we did we modeled evolution in the chemostat We see that evolution is pretty relentless. So if you give it if you keep giving it mutations The chemostat will drive the K low and lower and only when you run out of mutations Well, the evolution actually come to a stop So the chemostats environments. They're really aggressive and they basically would drive this K to the boundary of what's physiological possible Until you sort of hit suddenly a constraint that lowering the K would change other traits Now in the batch culture environment, this is an environment. That's like the long-term evolution experiments We have these growth cycles actually even if you give it a lot of mutations all the time evolution sort of stabilizes by itself and That was sort of from the evolution perspective the most interesting mechanism to be focused on that quickly sort of the simulation is simplified in the Basically, we have some some growth cycles going up and down in the background and then we sample Mutations and then these mutations can expand and replace the previous type new mutations appear Sometimes they also fail to fix and the way we calculated is that for every mutant that appears We calculate a selection coefficient and then a fixation probability and then basically with a certain probability of reject or accept that mutation and this Something that I wanted to just highlight as a teaser. So calculating the selection coefficients was a key technical step and We break it down to a basic unit one growth cycle Say this is somewhere in the middle of the competition where they're 50 50 for each growth cycle We can calculate the selective advantage from the beginning to the end The number that we calculate here is this S. It's the selection coefficient. It only depends sort of on Frequencies at the end and the frequencies at the beginning we were We did not care sort of what happened inside the growth cycle and so we Decided to not Simulated but instead calculate the S and just given the traits and the initial frequency we can directly predict the final frequency Using an explicit formula and on the tutorial on Tuesday I will talk about a bit more about this because this is an explicit representation of selection pressure Sort of understanding how this object changes with concentration can tell you how in which conditions say a mutant on G max Is selected more than a mutant is selected on K Okay, there was a key assumption in our model. That's basically how we sampled the mutation. So We draw a random mutation effect And that is from a uniform distribution that has a maximum value of kappa and What we assume is that this Effect does not change. So here you can get plus minus kappa and here you can still get plus minus kappa This is Not realistic, so you would expect that as the trade changes also the range That mutations the effect that mutations can have would maybe shrink so kappa would get smaller However, it's what we are interested in is basically more a maximum possible evolution So if you give the process always new mutations that have this fixed relative effect What is the maximum possible evolution that you can get from selection and What you see here is Trajectory, this is a population that starts at a certain ratio k to r0 is this highly unadapted The k is much higher than the environmental concentration used in the spatch culture It quickly goes down and then stabilizes. You can see there's some stochasticity here. This is because of the sampling and Stochastic probability of fixation that we use the One thing to say about the time scale. So these is this is 50 times the population size So at this point we Over this time scale. You also see sort of the fixation of some some neutral mutations at the end There is a threshold here that forms a plateau we can calculate it But I first wanted to give you sort of the intuition what happens here in the growth cycle So we start in a situation that is highly unadapted where we have a clear exponential phase And then this deceleration at the end if you'd measure your d you would see it in this curved shape here And if we in this situation calculate what would 1% on the growth rate and 1% on the k A 1% improvement in each of these traits how much fitness would that give you we can break it down by these two traits This is the total fitness that a 1% mutant in each of these traits has and You can see that this much comes from growth rate and this much comes from the K and In this case we can see sort of the K is actually more strongly selected because the 1% in the K gives you a larger Contribution to the relative fitness. However at evolved stage now your Current K is already much lower than the resource concentration, which you mean you have this very sharp arrest at the end The growth is now very much like in a kink You've basically evolved the deceleration of a and all the selection that is left is now on the maximum growth rate And this is the the mechanism By which we get this plateau that you basically in the beginning have a lot of selection on the cave But this pressure sort of as you adapt You This face gets shorter and shorter you expose the trade less and less during the competition and you have less selection We get a scaling relationship That says that the evolved trade depends on the concentration that you would use for your evolution and the population size at the bottleneck This one last feature That's interesting here That's asking are these two parameters independent You said that the selection coefficient was also related to G max, but yeah, so for the evolution we So we've seen in a trade distribution right that these trades are largely Uncoordinated So we could assume that they evolve independently and to make things Can assume an independent Mutation effect on the two trades and to make things even simpler we just assumed a mutation effect on the K So the K of the G max in this background is not evolving No, and your experiment do you also allow cell to die between one spike and the other? So you just study the growth and the stationary phase So we have death in form of this dilution But not within the growth cycle. Okay, so we get this this a scaling relationship and this is Basically what the hypothesis said right you have your environmental concentration and your wolf trade is proportional to that However, there's also this additional factor of the population size at the bottleneck that sort of interferes with it and and the evolutionary terms this is a balance between selection and drift at the bottom and There's one Very subtle detail That these two parameters could actually not be independent depending on how you run your evolution experiment so this is One way to transfer between growth cycles is I have another question. So can you get the pre-factor? Between K evo are zero. Yeah any because then you can test it with values There are values from effective cooperation size of different. Yeah, yeah, we have the we have the pre-factor There's a pre-factor that also depends on the maximum mutation effect you can have and then there's a local earthquake term So the problem is we have Undetermined this so we actually don't know the concentration that Equal I would experience in the gut and we don't know if it's a chemostat or a batch culture for the where we know this really well is the LTE and And the LTE what you see is that the concentration they used was Too high to create a selection pressure on the K so to basically Cut the short these two things depending on how you transfer they can be correlated And this is one way to transfer is to reset to a fixed biomass of your first growth cycle one day And you reset to the same OD Now if you would use a larger resource concentration You would still reset to the same OD in this case the bottleneck size and the resource concentration are independent And you can really get this scaling relationship However, most of the experiments work this way where you reset with a fixed dilution factor So growth cycle with more resources like the right one here also gives you a higher population size and you get this positive correlation between the two things and If you put in the mouth and you look at the factors in the formula you can see that this actually cancels out What we then reconstructed is basically an inverse problem this is the Distribution of case that we've seen in the coli data and we asked with what sort of Glucose concentration would they be compatible with and here we assume basically We can estimate mutation effect from the LTE Not a direct test, but we For this you would really have to measure spontaneous mutations But we basically assume that the thing that we observe in the LTE is At the evolutionary steady state So this is the 140 micro model that they're using here and now if you would Take An E. Coli in your data set and ask which resource concentration that it would evolve on It depends what kind of environment you assume If it's a fixed bottleneck biomass you can say well these E. Coli They came from a higher concentration environment but if it's a fixed dilution factor you can see that This E. Coli here is compatible actually with a lot of resource concentrations So in this sense, it's not a biomarker for the environment So even if you know the wall of trade it's compatible with a lot of historic concentrations Okay, this is I Would say the evolutionary high point I think especially interested Maybe in this context to discuss more about the trade-offs and if you have any questions Yes, I have to happy to take them