 There are no more hands. No, yeah, there's Cornelia. And there is a question in the chat. First time I see it. Okay. Thank you for the great presentation. Please scan the mixing, deregulate the sequence in the modeling. Yana. I'm not entirely sure I understand the question, but perhaps Monday or Adiaha can rephrase their question while Olivia is giving her talk, and then we can discuss it later. Yeah, maybe it's better. So here is Olivia. And she is a PhD student at the University of Washington, and she has a great method to measure conjugation, and I've seen her talk at Plasmids, and I was like, wow, we need to have Olivia at the workshop, and finally there she is. So please, Olivia. Thanks, thank you so much. Can you hear me okay? Okay, yes. All right, so hello everyone. I really want to applaud Alice and the organizers for the conference and everything you put together. Thanks, Alice, for bringing us all together and doing all the hard work of organizing, which is I know from limited personal experience that is challenging. So, but yeah, today I'm really excited to share with all of you. Kind of Yana had a great talk and talked a lot about why I also am like her, and I care about transfer rates and estimating them accurately and why accurate estimation can be important and help us not get misled about the data we're collecting. So with that said, I work in the lab with Benjamin Kerr at the University of Washington. I'm a six-year PhD student also graduating, maybe moving on to a postdoc because it's kind of similar to Yana in position, which is kind of fun. So I want to thank everybody that was on this project first and foremost, it was really close collaboration with my advisor, Ben Kerr, also with Ava's Topps Lab at the University of Idaho and Ivana Bozik's lab at the University of Washington. And so I also am going to give a little zoom out about why I'm going to make a plug for the estimating conjugation rates are important. And I kind of come at this from a similar but slightly different angle. And I like to use this example of COVID-19 pandemic because it's a familiar topic to everybody and kind of gives us some intuitions about modeling and why parameters are important in them. And so during the pandemic, we're just really, there was an extraordinary effort early on for us to try and understand how fast the disease was going to spread in the population. And so to do this, most of the models were extensions of some standard epidemiological models and Alice gave us some interesting intro to all of that. But this SI model just is simple we are tracking two populations, a susceptible pool, people with not that don't have COVID and then the infected individuals. And the model determines how fast susceptible individuals are going to turn into infected individuals and that's dependent on this transmission rate that we call beta. And this, of course, we all know depends on actually making human contact with somebody that is infected. So you have to have some human contact for transmission to occur. And so we need to add this to our model and we can take a slice out of our chemistry textbooks to do this and we're gonna use the law of mass action. And this just allows us to use the density of the two populations, multiply those together with the transmission rate parameter. And that will kind of tell us how many of those infected individuals will be created over time. If you're not familiar with transmission rate, you're probably more familiar with R0, which is like this basic reproduction number that we kind of focus on when we think about pandemics or viral spread. And you can clearly see by this equation that I'm showing you here that essentially beta is really important for R0. And why I bring that up is because early in the pandemic we all remember these forecasting models people were using about how fast COVID was not spread and they were sometimes good and sometimes not very good. And a lot of it has to do with the parameters we use underlying the models to give us good, accurate or potentially inaccurate predictions about the biology. And so what I think is really fascinating is that the way we model conjugation and we think about plasmid spread is like really similar, like almost the same. So when we care about plasmids in our communities that we've heard about in the gut or in the hospital settings or in wastewater as we've heard a lot this week, we wanna know how fast these plasmids are spreading through our populations over time. And so similar with the COVID example, we're tracking two things. We're tracking our plasmid-free types and we're tracking our plasmid-containing types. And the way they turn into plasmid-containing type is the transfer rate parameter that we are all interested in knowing, estimating correctly. And this is also density dependent. So for conjugation, which is just one mode of how horizontal gene transfer happens but conjugation is cell to cell contact dependent. So we add that law of mass action parameter into our models and then we can model this and how fast plasmid-containing populations are gonna come up over time. But transfer rates are not trivial to estimate for many reasons but one of them is that there isn't just one transfer rate. You can't say this plasmid has this transfer rate or you can't say because they're gonna be very dependent on the environment and the cells that they're around. So to kind of illustrate this and make kind of an analogy, we know that there's transmission rates across species for viruses just like how we probably, the COVID pandemic came from maybe a species like a bat and that transmission rate is quite different from human-human transfer of the virus. And so this is similar in our microbial communities but much more relevant because we think about these species being in close contact with one another all the time. And so here the transfer rate of the between the blue species is probably quite different than the donor, the plasmid is transferring between the red and the blue species. So how do we estimate conjugation rate? Yana gave a good example for the intro of this and I'm just gonna go through this really, really briefly but I think about it in three phases and I'm gonna kind of walk through the mating ass in very specific ways. And this will hopefully help us understand how our new method is quite different framework to how to think about how we estimate conjugation rates and makes it so that you estimate kind of measuring different things in the laboratory. So again, we mix our donor and recipients together in a tube just like normal and as we call this a mating assay and we're just gonna track our populations over time and they're going to essentially grow because there's gonna just be division of your donors and your division of your recipients over time. But at some point at this critical time point you're gonna have a conjugation event happen and you're gonna create this first trans-conjugation cell which is what I'm showing you right here. And this is going to happen at some critical density and gonna matter for what the donor recipient density is matters and then what that actual transmission rate between the transfer rate between the two cells is. And here I'm representing the trans-conjugation with a blue cell because that's the recipient but it got the red plasmid and then I just fill in the cell with purple just so you can easily track them in the presentation. All right, and then as we let the tube go we're adding two additional dynamics in our tube that are important. The trans-conjugations are now growing because that population, that third population has been created and importantly that third population now can donate its plasmid to the recipient like Yana was saying earlier. And so we have these five kind of key events that can happen in the tube as it incubates through time. And these dynamics that are occurring in the mating experiment were modeled using a set of differential equations by Bruce Levin and colleagues where each population type is a variable in the model. Yana kind of described this but the three populations have exponential growth and we're showing the growth rate parameter with this brown side parameter. And it's very importantly the same across all three populations in the original model. And then we also have trans-conjugates are being created due to plasmid transfer events into recipients and from donors. And those are happening with this transfer rate and gray again same for both types of events. Okay, so later on we got the Simonson method because they found an analytical solution to these sets of differential equations like Yana said and I will refer to this conjugation rate as the SIM method. And so what we do with the SIM method, again, you can see in here this gives you everything in the laboratory that you need to measure. So we have an initial population size, a final population size and then importantly your three populations you need to get an estimate of their density at some critical point in time as well as the max growth rate, just like Yana said. Okay, but our method updates some of these assumptions. The first two are similar to Yana's. So I'm gonna go through them really quickly. We know that things grow at different rates especially if they're different species like if I grow my Klebsiella in the lab and my Echoli in the lab my Klebsiella grows a bit faster at least for me, quite a bit faster. So we care about that. So we update the growth rate parameters and we allow there to be population specific growth rates and I'm showing you that with the red, blue and purple side parameters. We do the same things with the conjugation rates especially because Yana showed some good data that within species conjugation rates can be quite different between cross-species conjugation rates. So we have these population specific transfer parameters in our model. And this is the diversion with other previous estimates is that we use a stochastic branching process framework to derive our metric rather than a deterministic approach which is what other methods use. And we incorporate the fact that conjugation is a random process in your populations and this is the case with mutation, right? So let's make an analogy to that because it's a bit easier to understand. So we're gonna track a population growing through time. We have a wild type cell and each cell when it divides there's a probability that a mutation is going to occur. And for this population, the first mutant arose here and I'm highlighting that with purple halo and then this also goes through clonal expansion and those mutants divide through time. But the important aspect is stochasticity. So if we ran a few populations in parallel for a short amount of time, what we're gonna see is that some mutations some populations do not acquire mutations within that timeframe and other populations do. And this heterogeneity across different population is kind of highlighting the random aspect of mutation and what's kind of the classic key observation or key intuition that the Luria-Dellpark approach has and what they actually use to estimate mutation rate. What's really cool is conjugation rate is conjugation events are similar. They're also transforming the genetic state of the cell because you're taking a recipient and you're adding a new DNA element. So it's a type of genetic transformation. But instead of tracking just the blue population we also need to track this exponentially growing donor population through time. And that's kind of like the difference between mutation and conjugation. There's these two population types that are particularly important. But when you can also look at mating assays, those pretend they're all like nine mating assays in the lab and you can see that some of them if you run them for a shorter period of time will not have a conjugation event occur. So no trans conjugates are present. And then you have some populations that do have trans conjugates. And this is really similar to the mutation process. So using this stochastic branching process framework and the updated model, we derived a new estimate for the conjugation rate which we call the LDM. And it stands for Luria-Dellpark method because we were really inspired by their approach to estimating mutation rate. And the important distinction with the LDM is you do not need an estimate for the trans conjugate density. This has a lot of advantages when you're doing lab work and I'm really happy to talk about, go into that in detail, but instead I'm gonna kind of highlight what you do actually need to measure for the LDM. So you need an initial estimate of the donor recipient densities and a final estimate of the donor recipient densities, but there is no trans conjugate density estimate. Instead we have the P naught right here. And P naught is actually the probability of having zero trans conjugates. The easiest way to think about it is that what's the probability of getting one of these gray squares? So the probability of no population that has no trans conjugates. And the maximum likelihood estimate of that is actually just the proportion of populations within this array that don't have trans conjugates. So to kind of show you very simply how we do this in the lab, you just make a bunch of mating assays so you just make sure donors are recipients like you were before and you're gonna just ignoculate all of your wells in your 96 well plate. You're gonna allow them to grow and incubate for a short amount of time and allow transfer to occur. But transfer importantly, because you're only running it for a short amount of time will only occur in some of the populations and not in others, which I'm showing you here, one population with trans conjugates and one without. And then you add trans conjugates selecting medium to your plate essentially dilutes everything. So you can kind of like, you're like stopping conjugation because you're like diluting everything down and so making things less dense and you're adding things that are going to inhibit the growth of the donors and recipients. And so anything that has trans conjugates with this new medium added will grow up to a turbid culture. And then after this incubation you're gonna be able to identify the populations that had trans conjugates and then the populations that didn't. And what's great about that is you just look at your plate by eye and you're like, count the number of wells that are not turbid and you just make a fraction and you say, okay, here there was 31 populations that were not turbid out of 96 and that gives you your P-naught estimate which can be used in the equation I showed you before. Okay, so that's great. We have a new theoretical framework, new analytical estimate and then a laboratory assay. So how accurate is malaria-delbrach method compared to other approaches? That's a good question to ask whenever you make a method, right? So I'm gonna show you some stochastic simulations very briefly. And then my most exciting thing to show you if you were at Closet's Roundtable is that our new experimental data at the end. So I'm really looking forward to sharing that with all of you. So the simulation, so briefly we just run, here I'm showing on the Latin deterministic simulation. So you just set some initial donor and recipient densities, you pick some conjugation rate and growth parameters and you run a deterministic simulation. This is what other people assume in their methods is that things happen at this like average deterministic, just means like your average trajectory that you would get. But we made a stochastic framework because that is similar to how we actually, what we do in our theory, you allow things to be random. So what you do when you run it, one of the stochastic simulations is that you're gonna get a trans-conjugate trajectory that deviates from the average. And that could be because the first trans-conjugate showed up later in time than the average expectation. If you ran another simulation, it might show up earlier in time as I'm showing here. And so what we do is we use the simulated populations to calculate the conjugation rate using both the LVM and the SAM equations. In the paper, there's actually other metrics that we use and that can be found in the supplement if you're interested in comparison with other metrics that are around. But I will reiterate here something really important which is that again, the difference between the two equations mainly is that you need a trans-conjugate density to have. You need to have a trans-conjugate density that's not zero when you do Simonson. And for ours, you need to have proportions of your populations that do and don't have trans-conjugates. And so the timeframe at which you can assay these to do these metrics are different. The LVM can be assayed where you have a proportional population without which is gonna be around this timeframe. And then Simonson needs to happen after you already have trans-conjugates showing up. And that's gonna be an important thing to keep in mind when you interpret the simulation results. So for the sake of time, I'm just gonna show you one simulation scenario that is particularly relevant to me because I'm interested in microbial communities. And so here I'm showing you where I set the cross species conjugation rate to be much lower than the within species conjugation rate. And what we're trying to estimate is gamma D, which happens to be the cross species conjugation rate in your assay. So the one that's happening between donors and recipients, not the rate that's happening between your trans-conjugates and your recipients. So we set that, we set a conjugation rate, which I'm showing you here. And then we're gonna use our simulated populations to look at our two metrics. What you can see with the LVM is that it's accurate over time, which is great. And then what you see with Simonson is that you get increasing inaccuracy as incubation time increases. The intuition for this is that, remember those three phases I told you about in the mating assay where you only have donor and recipient growth, you have that conjugation event occur which creates that third population type. And then there's the phase where trans-conjugates are present and you're having trans-conjugate growth and trans-conjugate conjugation occurring. The longer you incubate, the longer the trans-conjugate event types are gonna contribute to the accumulation of that population. And that's essentially why you're getting over, you're getting inflation and overestimation of the donor conjugation rate through time. Okay, so let's move on to our laboratory experiment. So I'm gonna show you a cross-species case study where I set up mating assays in the lab between Klebsiella and E. coli and with an in-gef conjugated plasma. And here on the x-axis, I'm gonna show you what I got for the LVM method side by side with the Simonson metric in the lab and then our estimates on the y. And this is what we got. And so you can see there's a huge discrepancy between the LVM estimate and the Simonson method where the Simonson estimate is a few orders of magnitude. It's quite shocking, above what the LVM got. And so there's some inaccuracy seeping into here. But one thing that could explain the overestimation, I kind of set you up for it with the simulation, is to think about that, what is the within-species conjugation rate? So if the trans-conjugate conjugation rate or the within-species conjugation rate, so with an E. coli is much higher than the cross-species conjugation rate, our simulation results suggest that that could potentially be making the Simonson method overestimated. And so what I did is I took the LVM metric and measured the within-species conjugation rate to see if it's higher. And in fact, it is by a lot. It's about six orders of magnitude higher with any coli than I got when I did my cross-species conjugation rate estimate with ClpCl2 coli. And so notably, this supported my hypothesis that Simonson was overestimating the cross-species conjugation rate due to potentially a higher within-species conjugation rate. But I did one more test to kind of get some more supporting evidence for my hypothesis. And my test came from the intuition that I started to get from the simulations, which is that what happens with incubation time is you get more and more overestimated. So I ran, this was a traditional Simonson assay. And the traditional Simonson assay includes a 24-hour incubation time. And so what I did is I ran a truncated Simonson, so I shortened the incubation time a lot to see if that would result in the estimate of Simonson coming down and getting closer to what the LVM gave me. And in fact, we did see that with our truncated assay that the Simonson estimate came down. And that was our second piece of experimental evidence that supported our hypothesis that the Sim estimate was inaccurate due to the asymmetry between cross-species and within-species conjugation rates. So I was pretty excited about this data. So just to wrap up in conclusion, so we developed this new LVM method and we think it really offers some new possibilities to be able to accurately measure conjugation rate between many types of plasmids, species, and in fact, many different environmental conditions that we might be interested in. Particularly what Yana was talking about where we're kind of need to understand how temperature and different biotic or abiotic factors actually affect these rates. And we think our method offers the possibility to look at some of those things and accurately. So here I showed you, we derived a new estimate. We checked accuracy with and precision with our stochastic simulations. And then we applied our laboratory protocol to a cross-species case study alongside what has been kind of the longest running gold standard approach Simonson for some decades now. And I want to just make a plug, an important plug that I think the most important thing that I learned with this project is check the assumptions of your model when you're running, when you're trying to estimate things and check the assumptions in the laboratory too. Because there's things that can bring bias into your estimate because of how you're running things in the lab, are you running them correctly? Are you getting things into a constant growth rate, exponential growth? Are you using a well-mixed system? And are you executing it in a line with how the model actually is telling you that it should be ran? I'm really happy to go into all the assumptions that I think should be checked because I have definitely seen that if you violate any of these assumptions in the laboratory when you execute it, it will give you quite different values for your transfer rate, which could be really misleading, especially when you're trying to compare things in the lab. Does this have higher conjugation rate than that? Well, it's not a systematic deviation and potentially if you're violating an assumption, it's not going to just systematically elevate or lower. It's going to maybe change the rank order of your conjugation rates. It might be giving you the wrong answer. So just kind of a cautionary note and something that I've noticed of being like, wow, if you do one thing, even a little bit different, it can give you quite different estimates, which is like, okay, we've got to be really careful. And another analogy I like to make that I feel like kind of communicates how important the laboratory execution is, is like the rigor we apply to RTQPCR, right? When you do RTQPCR, you know that you need to check the efficiency of your primaries. You need to have more than one reference gene. You need to do a concentration gradient of your DNA. And so when we're looking at how to execute those protocols, we have very stringent criteria that we follow and I think measuring conjugation rate needs to move sort of in that direction so that we can be really confident in the estimates we're actually getting in the lab. And with that, I really want to thank everybody on the team being my sounding boards with all of my questions and problems I ran into along the way. Thanks to my funding sources and thank you all for hanging on and listening and thanks to organizers for a great week. And I'm really happy to discuss anything that I talked about today. Yay, this was great.