 But I'm glad it wasn't. I'm glad that Kerry talked about phage because I got the impression that this is sort of the affirmative action in the end of talks that we're going to talk about bacteria phage. And I think I'll try and convince you why it is really so important to really consider phage. We specify Google Hangouts because Google Hangouts have been very important to our collaborations. It's made everything, it made collaborations really quite wonderful. And we can't share coffee yet, but maybe soon we're going to get a beaming down technology. This motivation for this is really these two undergraduates. The first, this is Nielong Shaw and Watkus Chaldery. Nielong is an Emory undergraduate. Watkus is a graduate student from Islamabad who did his research in my lab. And Marish Pleska is from the IST in Vienna. Ingrid McCall is our lab manager, amazing, amazing lab manager. Howie Weiss is our resident mathematician, sort of an affirmative action thing. You want to have one around, but you don't. And Jim Bull is my good friend. And there's two pictures of Jim Bull one eating breakfast, which he and the other one was a couple months ago at the National Academy. And so the work is about that. You'll see what I'm, anyway, so the quest outline, we're going to give you a perspective on phage. When I carry, I began to start that, we're going to continue, consider lytic phage, the phage that are sometimes referred to as virulent, and I'm going to present a hypothesis about how they're maintained in bacterial populations. And I'm going to talk about temperate bacterial phage. I'll give a little bit more background. That is the ones that form lysogens and are vertically transmitted. And then I'm going to consider the two of them together. And these are pictures of phage and eating bacteria and doing nasty things. I love this, this kind of phrase that is bacteria phage are the most abundant organisms on earth. And then they give these numbers like 10 to the 30 bacteria, 10 to the 31 phage, whether it's 2.39 times 10 to the 30, I don't know. But phage talk start with this, sort of like antibiotic talk start out with antibiotic resistance is the worst thing ever. This was before the election in the United States in November. But I won't start my antibiotic talk, it's a great career opportunity. But phage is certainly abundant, whether it's 10 to the 31 or not, I don't know. But they are all over the place, you know, you can go, we're going to go snorkeling later when my people going snorkeling don't realize I'm there to get some phage and find some in the Adriatic. But they're really abundant. But we really know shit about them, shit is a technical term for those of us that work with E. coli. We really know nothing about what they do in natural populations, very, very little. The first phage that's to be discovered was by a guy by the name of Hankin in 1896. And there was something in the Yuma and Ganges River that lice, vibrio, cholera and vitro. And there was a first evidence for phage, whether they're regulating the densities of populations so we really don't know what they're doing. And that's really kind of curious in that did phage actually regulate the densities of the bacterial populations? Do they contribute to the species and strain this, what do they contribute to the diversity? There was all of this discussion, at most of this talk was considering diversity, but really didn't consider the role of phage. And they're out there all the time. What are the contributions to phage that horizontal gene transfer? I mean, we know we could get transduction all the time. What about the conditions under which phage will be maintained in bacterial populations? What are their, what I'm going to call their existence conditions? So what conditions will temper it in lytic modes of phage replication be maintained? These are the kinds of questions that I'm going to be talking about. The last two is going to be the main focus of what I'm going to be talking about. And we also have been doing phage therapy, the question, these are phage that came from, if you need phage, they came from Tbilisi, Georgia. There was an phage institute in Tbilisi, still is, and at one time Russia, the whole former Soviet Union, phage were a dominant mechanism for treating and preventing infection. Did it work? Did it not work? And this year, although I don't have time to talk, we met a number of people who have been getting phage therapy and are very much, and one of them went to Tbilisi and brought us back all these phage. I've been there. I also got phage and some of the phage we're using for experiments are coming from this. We recently published a paper, I'm sorry, about using phage to break up biofilms for the joint action of antibiotics and phage. The antibiotic resistance has gotten people panicked and phage is a resurgence of phage. I think it's sort of interesting to look at how you could break up biofilms using anything to break up biofilms for joint treatment with antibiotics. It's not what I'm going to talk about now. This is Frank Stewart. Frank Stewart is a mathematician I worked with for many, many years at Brown. I started when I was an assistant professor at Brown, a wonderful, wonderful human being and mathematician. And so there's a lot of what I might call deja vu in this talk, but there was a lot of deja vu in this whole meeting that is these questions that we were asking. And Alan Campbell, who played a major role in understanding how Lambda works and Lysogyny wrote a paper in 1961 entitled Conditions for the Existence of Bacteria Phage. How do bacteria phage maintain their populations in the presence of bacteria? Now there was something that came out of this paper here with Frank, the one, that's not what I'm going to do, that this one where we took about, we're interested in resource partitioning and the conditions for maintaining populations. And one of the things that came out of it was that if in fact the number of say bacteria N, it has to be greater than the number of phage, but less than the number of phage plus resources, meaning we can theoretically, by putting phage into these communities, we can totally pack the communities at least in theory. So therefore I was really surprised that all the talks that we had about the structure of communities and microbiomes, which is another career opportunity, people are not looking at the role of phage. I mean, I don't know what that role is, but it seems to me something should be looking at it. That is, if the number of say prey has to be greater than, prey species, no, no, no, number of species are number of genotypes, they're number of clones, has to be less than the number. So you add a third trophic level, you can totally expand the diversity, at least in theory, whether it's done in reality, I don't know. I'm thinking strains, clones, I mean, if you take E. coli, there's more diversity in E. coli than in all the mammals. So I don't want to get into the philosophical of what is a species, because that's a philosophical and semantic question. But there's tremendous amount of diversity in these organisms, so how do you maintain all that diversity? Right, that would be probably, that's one practical devion, whether it's species in the same way that, you know, who mates with who, and who could produce fertile offspring, they don't do that at all. Right, yeah, I don't want to embarrass you about that set stuff. Anyways, this is the life cycle of lytic phage, basically the sort of the standard lytic phage. Some don't kill their cells, some just ooze out, but they're growing at the expense of the bacteria. So the bacteria phage enter the cells, they then basically turn the bacteria into a machine to produce more phage in the bacterial lice, in the simple interpretation, so we're infecting the cells and we're producing say 50 or 100 phage particles for every infection. And that's the concept of a lytic phage, that's the classical phage T2, T7, and so on. This is, and then there's another class of phage, which are called temperate. Temperate phage have the, they do the lytic cycle, so they replicate that way, but there's a low probability that when they infect the cell, they will incorporate their genome into that of the cell, and if they incorporate their genome into that of, whoops, that's not what I wanted to do. There's a light here, okay. If they incorporate their genome into the cell, then they have the possibility of being transmitted vertically. So they have the virtue of being transmitted horizontally, entering a population, and then they can be transmitted vertically. And then be transmitted in the course of cell division. Now, phage, in addition to killing bacteria, they're code for many, many characters in terms of the, the, the pro-phage. So Staphylococcus, for example, has two oodles of these pro-phage, these, these latent phage. But if you look at it, you know, the bacteria would be quite nice. So, so, the first one was, was a bordatella. I mean, the, the theory, a quantum bacterium diphtheriae. The, the quantum bacterium diphtheriae is a virulent unless it has a pro-phage. So the virulence is coded for by a pro-phage. Cholera is a virulent. The toxin is coded for by a pro-phage. Why are all these toxins coded for by phage rather than chromosomal genes? Why not plasmids? So that many of these toxins are coded for by phage. 0157, E. coli, that gives you the hemolytic uremic syndrome, the phage code for the toxins. Not, so the, so it got nice bacteria in the, in the sort of nasty phage. Tempered phage have certain virtues. I mean, they, they can be transmitted infectiously, and they can become established and maintained at any density once the, because they don't have a lower density as you would for, for horizontally transmitted. And they can directly increase the fitness. So why aren't all phage temperate? Why are some phage obligatory, lytic? I mean, and part of the answer, and maybe this would have, I use the word cheating, is we could get mutants of temperate phage that are lytic. That is a temperate phage when, when a cell is, gets a pro-phage, it's immune to super infection with that phage. So that once it gets the pro-phage, it now won't be infected by that phage. It's basically resistant to that phage. Immune is more accurate. But we can get mutants that will be cheaters in that sense, in the, that they can then replicate on the, the ones with the pro-phage. So the big issue that we had, and starting in a paper written ages and ages ago, is, you know, why be temperate? That is if, in fact, you can have these, these lytic mutants can occur. Well, it was a paper we wrote a long time ago, and I was at the time, we're interested in this question of existence conditions. And then I got a little bit fickle, I got onto other subjects. And it wasn't until these two grad, this undergraduate and graduate student came, I said, well, let's go back to this question. We wrote just a theoretical paper. Writing a theoretical paper is kind of not, not as satisfying. You know, it's, maybe it's like masturbation. It's not quite the same thing in that it's getting into doing the experiments. And then, and, you know, the experiments are really what I'm into. I love modeling, but it's not the same. And you really want to do the experiments, or have somebody do the experiments for you. No, no. So, that's what it's, so that the, the issue that, that I'm going to first, the difference is that, well, phage are, are, are maintained in, when you do an experiment with phage, you do, in fact, with population of bacteria and phage and chemistads for serial passage. What happens is that they're maintained continuously. And temperate phage clearly exists. So that is to say, so we're not going to refer to them as problems. One, my hero, Andre Levovsk, one of his comments is, nature does not have problems, nature only has solutions. So obviously, we're not going to say, I'm not going to conclude from based on the models that phage couldn't exist. Or if I, I did, and, and even if I had some theorems and lemmas and stuff like that, we'd have to deal with the fact that they do exist. So the, the questions I'm raising. What we see when we do experiments, and these are experiments going back a long, long time before many people here were diploid, but, but basically, when you take, this is a phage T7, the one that, that you work with and, and, and a wonderful student, my first student, Lynn Chow. And you could see that, that in, in this situation, we have, we start out with sensitive bacteria, we then have phage. We then get mutants bacteria that are resistant to the phage. And then we get phage that can attack those bacteria. And then we get bacteria that are resistant that can take over. And you could see it in this case, this is a chemist out that went 1200 hours with the phage being maintained, the dominant population with, with phage and the bacteria will maintain that this low level. Not low in the 10th to the 6th or so. But once you get resistant mutants, the, the resistant mutants take over and the bacteria and phage continue to co-exist. So that now the dominant population of bacteria is resistant to the phage. And this occurs in, in, this is E coli T2. We get the same thing. Within a short order, the dominant population of bacteria is resistant to the phage. This is studies with cholera, librio cholera, we're interested in the role of ca, phage and regulating the densities of cholera. So we're, we're interested in the dynamics of phage as much, but rather the practical applications. And there too, the phage, the resistance evolves, but the phage continue to be maintained. The, this is pseudomonas. In this case, there's a whole bunch of cultures walk us. Did these experiments? We have, and in most of the cases, the dominant population of bacteria are resistant. And, and, and this, this is sort of what you see. And nevertheless, in most crotch cultures, the phage are maintained. So the phage theoretically can't be growing on these resistant bacteria. And nevertheless, their populations are maintained. This was serial transfer, the others were chemistat. So it doesn't matter. And we're now doing it in, in, in film, biofilms and we're still getting the maintenance of phage. This one here is streptococcus thermophilus. It's a whole other seminar where, when, when people discovered, you know, that, that, people, actually Rudolph Barangiu showed that, you know, that CRISPR, this is sort of a, there's a whole enterprise now. You probably think of CRISPR-Cas as, as a tool of capitalist molecular biologists, where now it's a major thing in terms of genome editing now. And, and there's a lot of concern about, you know, changing humans with this system. Well, this, this CRISPR-Cas is, is an adaptive immune system in bacteria. And we, we did these experiments trying to explain how you maintain this, this situation where you're getting a, a continuous co-evolution occurring. And in, in, in this particular bacteria, which we got from Rudolph, it grows in, in, in, in, is the one that produces yogurt. It's streptococcus thermophilus. And so that's why we were growing it in milk. It's the ideal medium for it. And you just go get some, we, we gave them skim milk. We didn't want them to get too fat. But, you know, you could grow them in milk. And the only problem is that you're ultimately sampling yogurt. So that you put them in milk in one day, and the next day you got yogurt. So you have to then, to estimate the densities, you got to really vortex them. Pretty amazing to me how rapidly yogurt is formed by this, this phase. And there was a lot of interest in it, from a practical perspective of that phage contaminations are a major problem in the dairy industry. That is, you know, you have 20,000 liters of milk and you're going to make some cheese, or, or, and then you get phage contamination. And so it doesn't prevent it, but it puts it off by many, many hours. And therefore it was economic. So there's a lot of interest in, in Rudolph Behringer, a really terrific scientist, was in fact working with a company called Denasco, which made starters for yogurt. So there's a lot of interest in phage from the very practical perspective. Once again, you're maintaining this population of phage dominated by bacteria that are resistant to immune, actually immune in this case. So how are the bacteria, how are the phage being maintained? So that's the question I want to first address is how they can be maintained if they can't replicate on, on, on the, okay. So that's the first question. We can't say they can't be maintained because we obviously maintain them. Well, we do modeling as well as experiments and we use, and I, you know, on our website, I say we can, doing population biology and evolutionary biology without mathematical or computer simulation models is like playing tennis without a net or boundary lines. I mean, that's actually stolen from Robert Frost about poetry without rhyme. But you really need to do it. I mean, as Chris had to do it. And of course, each, so then in this case, so we have virulent phage, lidic phage, and, and called V, and we have sensitive cells. And we're assuming that we're producing resistant mutants at some rate. And then so that, that, and then you could turn it into a series of differential equations, which you can hum. There's a wonderful comment by, in a, in a, in a book review by Mediwar when he says to a friend, when you see a, a theoretical paper with equations, you, you, you can't understand. How do you read the paper? His friend says, I hum the equations. I find that to be the most devastating comment. But anyways, it's a very simple mass action model where we have, we, we have four, four bacterial populations, resistant, virulent, sensitive. And we are also assuming resources that there's a resource that limits the whole thing. And we're assuming, and by using resources, we can change the physiological state so that when the resource concentration gets low, the bacteria or the phage are not replicating as rapidly. In theory, this is what we would expect with the s, so we estimate the parameters quite independently. So you could estimate the nice thing working, working with bacteria and, and phage is we can independently estimate the parameters under the condition. So that the models are constrained even when you're doing numerical analyses. And so that this is, so this is what we would expect in the course of a short amount of time, the bacteria killed off, the phage then take over. And if I do serial passage, this is, if I assume there's a refuge below ten to the two, the bacteria, phage, phage replication stops. And we do this over, this is over, each one of these is at time. The phage can, we can maintain the absence of resistance. We're gonna maintain a population of bacteria at a low level. And it's gonna be, and, and the dominant population is gonna be resistant. If in fact we use the parameters we estimate and allow for resistant, virulent resistance, the resistance take over and, and the phage are lost. How, how are we maintaining them if in fact the models are predicting that? And so we did the experiments. We used, in this case, we, we used varieties of bacteria and phage. This was all done with staphylococcus, I mean E. coli. Using lambda, E. coli, uh, uh, uh, lambdas, I mean, this whole book's about, written about lambda. And, and, and curiously enough, we're running into new observations about the molecular biology of lambda, which I couldn't believe. I always thought it's all worked out. Anyways, I can mention that later. So we have E. coli, and they have lambda vir, a mutant lambda that can grow on lysogens. We have a lambda can, a, a temperate phage that has a canomycin marker so that when it infects the bacteria and we form lysogens, the lysogens are resistant to canomycin. So we could tell the ones that have acquired the prophage. And we grow them in minimal maltose medium or, or, or lysogyny broth, also known as LB. And then we're, and we're just doing serial transfer culture. So that's the, the entire technology, other than, you know, plating and so on. Now there's a certain caveat. How do you know whether bacteria is resistant or not? Well, what, the best test is you take a lawn of, you make a lawn, we take a soft auger and put it, put a high density of bacteria. And we drop the phage on there. And then, if in fact the phage don't grow, we say it's resistant. There's a caveat there, is that the assay, if you have a minority population of sensitive, if you have, say, 1% sensitive, it'll look like it's resistant. Okay, so that's one of the problems of how you would phenotypically estimate, determine resistance. But people this is used all the time and, and so, but this rate raises the possibility that the population may not be totally resistant. Now, this is one, one of the experiments where we take lidic phage, sensitive bacteria in this maltose medium, maltose is, is associated with the receptor site for, for lambda. And this is over the short term and over the long term, we're getting maintenance. That is to say, we're getting coexistence. This is a series of transfers. And so, this is in the absence of phage and these are dominated and what happened is resistance evolved very, very rapidly. So, we did many different experiments of this type. Occasionally, or some of them, the phage would be lost. In the majority of them, the phage would be maintained. This is just looking at the phage, the majority of them independent experiments were getting the phage maintained. And, and as I said, occasionally we're getting losses at different times. So the question we're asking is, how are the phage maintained if the dominant population can support their growth? All right. And so, there's something occurring. And so, there were basically four hypotheses. That is, phage, resistance, and gender is a fitness cost. And you can show that if there's a fitness cost, you can maintain it so that if it's sensitive, it can coexist. And I'll argue why that's not the case. There's a refuge on the walls of the flask. Two postdocs in my lab numbers of years ago. That is, we have biofilms and things like that. And phage, you're not getting at the, so that, you know, as long as there are walls on the flask, when you start out with sensitive, many of the sensitive bacteria are going to end up on the walls and they're going to continually putting in sensitive bacteria. The other is resistance is not absolute. And that there are a few functional receptors so that that is not really an absolute thing. And the last one is the one I'm going to argue for. And I would say it's a new mechanism. And it is in some ways. But people have made this before, including Max Stillbrook, who was sort of for the physicists here, he was the physicist that changed biology more than anybody else. He wrote a paper in 1946 saying that basically when you get mutants out of resistance, the phage continued to be maintained. It was something that would have been interpreted as lysogyny, but he didn't believe in lysogyny. So he goes through all this bullshit to avoid accepting the possibility that there's lysogyny. And one of the bullshit is that the phage are reverting at a high rate, the bacteria reverting at a high rate. So we're going to focus on what we call the leaky hypothesis. And the proposition that is if the resistant cells can, in fact, support the growth of the phage because they're producing sensitive cells, that means if we start out with a population of resistant cells, and there's a rate of reversion to sensitive, then the resistant, they're going to be maintained. To test it, we isolated 11 independent resistant mutants and put them in with the bacteria. And in eight of them, the phage were maintained. And in three of them, the phage were lost. So we're starting out with only resistant cells and the lidic phage, they can't grow on them. By all the physical criteria, they would say, but if you do the experiment, you start out with resistant, we're getting as many of them can grow. And so it's consistent with this leaky resistance hypothesis. That is that we're getting. So you start out with a culture resistant, your phage can actually grow. The question is at what rate does the rate of transition from resistant to sensitive have to occur to maintain the phage? How do you get that? So the way you get it, as you guys would probably appreciate, is you do a model and you ask, what rate do you need? And so what the model says is the rate has to be between 10 to the minus 4 and 10 to the minus 5 per cell per hour, meaning the rate of producing cells that the phage can grow on has to be that high to get the results observed. And the question then become, how do we estimate something like that? It's easy to estimate the rate of mutation to phage resistance. That's what Luria Delbrook did, which turned out to be the most single, most important paper in genetics and in a way in evolution, that you could get mutations to phage resistance. You just take a bunch of phage, place your bacteria on them and the ones that can grow are resistant. Easy to do and it really works. And you could estimate the rate of mutation by doing fluctuation, many different ones. Beautiful, beautiful experiment. But how do you estimate the rate of production of sensitivity? Well, I mean, one possibility is you get lots and lots of students and we'll have them tooth picking and then look at the frequency, look at 10 to the 7 cells and see what the frequency of resistance was. Well, it's really uncool. It's exploitation of students and toothpicks and so on. So that didn't seem to be the way to do it. The way that we do it was, in fact, using lysogeny. That is to say, if in fact that is this temperate phage can only infect cells that, so if there's a minority of resistant cells, the temperate phage can infect them and we'll see lysogens. So the prediction was that if in fact the temperate phage, that is, we take this population of resistant cells and ask if temperate phage can infect them and then from the frequency of ones that a temperate phage can form, we could estimate the frequency of sensitive cells in the population. We ordered more toothpicks, but this actually works. So we didn't need all the toothpicks. So the idea was very straightforward. And from the model of temperate phage, we can estimate the frequency, the rate of mutation because we could estimate the rate of lysogen formation. So that we can not only show that we can get this, we could estimate the rate. Admittedly, we have to use models. So the models then, if in fact, so the models make the following prediction. That is, depending on this rate of reversion, what I'm calling new R, we would get a certain frequency of new lysogens. So we start out a population with temperate phage and sensitive cell and no sensitive cells, but we have a rate of reversion from the resistance. And we would then predict that we can get so many lysogens. And from the frequency of lysogens, we should be able, a number of lysogens, we should be able to estimate that rate. We are just doing those experiments now. I should have pointed out that although that most, almost all you've heard in terms since we started with the lambda and the models is new. We're still in progress here. I'm pleased to say. And so we can get it. But the question is, there are alternative hypotheses. So we've gone through these alternative hypotheses. And so we didn't want to. OK, so we're going to argue. I think I put my slides in the wrong order. OK. So this should be the slide that I'll just talk about the alternative hypotheses and how we rejected them. So so far we only have one hypothesis that I'm considering this reversion. And if you look at this, these are 11 independent mutants. All of them can form lysogens. So they're resistant. We infect them with temperate phage. They all form lysogens, which is consistent with the idea of some of them being sensitive. And so they all form lysogens. And many of them can support the phage. So basically we're saying this is consistent with the leaky hypothesis. That is to say, we don't know whether the rate is high enough, but that's what we have to figure out. And the question is, have we rejected the alternative? That is to say, hypotheses are really there to be tested, not to be championed. So I gave four hypotheses. And I'm giving one hypothesis that we're supporting. OK. The phage resistance engenders of fitness costs. When we do the models, it takes a 35% reduction in fitness. We don't see that. I mean, they grow as well as the resistant in these cases grow as well. So that's inconsistent. What about there's a refuge on the walls? Well, there's no refuge yet, because the only bacteria we're putting in are resistance. So that's pretty much inconsistent with that. The third possibility of resistance is not absolute. That is to say, there's a low absorption rate. And that's what we're seeing. That one we can't really reject easily, but it's inconsistent so that if I have the theory and we have a very low rate of absorption, we're not going to get the observed dynamics. We're going to get the population dominated by the phage. And if the absorption rate is too low, we're going to not get it established. So basically, we're supporting this mechanism. Now, I'll let you look at this, because we talked about this at dinner a couple of times. Evolutionary biologists, in the past, we published something up in American naturalists. And when it came to the molecular mechanisms, in the past, we'd say some bullshit in the discussion, and then everybody was happy. We can't get away with that anymore. That is to say, people are going to ask, OK, you're postulating a mechanism. There's all the tools of molecular biology. You can't get away with that crap anymore. You're going to have to do it. And so this is what that's all about in reference at dinner that night when we were talking. That's when I got this idea. I call them the mechanism mafia. That is, you submit your paper and they'll say, this is really good, but what's the mechanism? And we can't get away without it anymore. Here's our tribute to the mechanism mafia. And I think the tribute seems to be the right word too, OK? There's a wonderful, I mentioned Andre LeVouf. LeVouf is the one that showed lysogeny, unquestionably that there really is lysogeny. And in a festrift to Delbrook, he was asked to talk about his most important contribution to molecular biology. And one of the things he says is it's really important not to determine what your most important contribution is, but rather to have somebody else tell you. Work by the agency. What? No, no, I'm sorry. 1902. Yeah, I'm sorry. Yeah, no, he's very young. He was amazing in many ways. That would have been even more amazing. But the last one I love, he says, prophages a remarkable indent, indeed, a molecule, I should say, for I have to be molecular, who is not. And I just sort of love that particular phrase. And virtually everything else, even his reviews are funny and warm and interesting. So I really recommend Andre LeVouf's writing. He was the major advisor of Jacob and Manot, among other things. And a pretty amazing, anyways. Actually, I met him once, but he didn't like mathematical models, but we talked anyhow. He was great. But anyway, so the question is, so basically we did what we should be doing is so we did the sequencing. We sequenced the genes that are associated with lambda. And the answer is that some of them are insertions, and those insertions reverted a high rate, which accounts for why we're getting. If you looked, we could see two things occurring with the lysogens. Some of the lysogens that we got when we infected the resistant cells were sensitive, meaning reversion. Some were resistant, meaning some sort of phenotypic mechanism. So we got, we're getting both. And when we looked at the molecular data, it looked like we can pretty much explain the ones that are reverting are often insertion sequences, which then are excised out at a high rate. And the ones that are phenotypically, ones that are not resistant are multi mutations, regulatory mutations that are probably screwing up in some of the cells. So I think, I don't know whether the mechanism mafia will be totally satisfied with our tribute, but I think we're at the point of saying we can pretty much explain it. The evolutionary biologists will because they'll just skip over that part anyhow, so we're fine. All right. So the conclusion that some of the mutants are real reversion, and we can explain the high rate, some are transition from resistant to sensitive phenotypic and presumably noise or what we refer to noise. And one of the things we work on is the phenomenon of persistence. That is, if you treat with bacteria, and this is a bacteria, this is gentemiasin, this is oxacillin, and oxacillin is not so good. This is staph aureus, that is, you don't just kill everybody, you get some survivors. Those survivors are what are called persisters, and those persisters, it's a whole industry, and people have lots of hypotheses about the mechanisms of persistence. And Chris was talking about it earlier, it's really phenotypic. That is, if I take these ones that survive, I could repeat the experiment and get the same rates. And we gave this in a paper where we have this thing, persistence, I wanted to use the word copacetic, which is a jazz term for satisfactory hypothesis for persistence, and we're just saying it shit happens. That is, it's like mutation, it's an error. It's an error and not inconsistent. So, we have this to get at the mechanism of phenotypic. Now, temperate phage alone, wonder what conditions will temperate phage alone be maintained. To adjust that, we did the modeling routine where we have temperate phage and the likelihood, and we could estimate the parameters of the model, and here's the model. And if we look at, forget the model, you're welcome to it, and so on. That is, if we look at what we would expect from the theory. The theory, if in fact, so we have, in this case, we have a population of sensitive cells infected with temperate phage. The phage density goes all the way up and the viscogens are formed. When we do the experiments, so I put dots on there, and we always have this trouble of telling the theory from the experiments, we're so good, I go, no, no, no. It's to see, it doesn't quite fit, but basically, within short-order, the dominant population is the phage go up, and this is the short-term. If I look at the long-term, we're getting new viscogens. We can't find the sensitive cells anymore, and there's some low density of phage, but the phage sweep through and then vertically transmit it. And if we start with lysogens, that is, instead of starting with free phage, we start with lysogens, which have a rate of induction. The model doesn't fit as well for both cases, and so the model doesn't fit, which means we, and I think models are in a way best when they don't fit, that means you miss something big about the biology and therefore you have. So we haven't figured it all out, but basically, lysogens are maintained, so that either way, whether you start with free phage or you start with cells invading a population that are already temperate, that goes through. Now to the question that was, in a way, motivated everything. So in the broad conditions, if you infect the population with temperate phage, the phage is gonna form a prophage of lysogens and it's gonna be maintained, and you're gonna see some minority population of sensitive, of free phage. Pretty close to what we're anticipating. But the question is, what about temperate and elliptic phage together? Will the cheaters take over? By the cheaters in this case, I mean the virulent mutants that can attack the lysogens. And there's so many possibilities. The temperate phage excludes the lytic, that's one possibility. That another possibility, the lytic excludes the temperate, which is what we were concerned about, that is that it's gonna sweep through the population and kill all and then it's gonna turn them into just tools and then there's equity. And so the question then became what happened? And so we have the extended model, which accounts for all of the other observations. And that too turns into a series of equations. And the theories predicting, first of all, if we have a certain rate of reversion from resistant to sensitive in the range observed, we're going to have resistance, this is resistant to virulent. So we have virulent and temperate phage together. We're gonna have resistant lysogens, we're gonna have phage and the virulent phage, the free virulent phage are gonna be lost and the lysogens are gonna take over. If we have a higher rate of reversion, then everybody's maintained in a stable way. That's the prediction. From the very simple mass action model, which doesn't account for structure and things like that. This is what happens when they're together. That is to say, so the dominant population is the total cells, when we examine them, they're largely resistant to the phage. We're getting resistant lysogens and the temperate phage are maintained. So that, so that we're basically the theories predicting stable coexistence and we're observing coexistence, not necessarily numerically identical. Now, as I mentioned that one of the advantages of lysogeny is that if there's selection for the genes on the prophage, then we're gonna maintain it anyhow. So that if we're selecting for the ones carrying the prophage. And that was really easy to do in our experiments because we had the cannomiasin resistance marker. So we have a cannomiasin resistance marker. We just put cannomiasin in there. And you could see when we do put cannomiasin in there, we're putting about two times MIC of minimum inhibitory concentration, that the lysogens just take over. So we're saying, and I'm sure the temperate phage in the world are pleased to know that they're not gonna be taken over by Lytic viruses. So that the theory and the experiments are saying with the parameters in the range that they can coexist and that's what we see. So in accord to our models, they will coexist and equity prevails, which is nice to, we can't extend it beyond our flasks, unfortunately. So these things, computer simulations and laboratory culture, we can have equity prevailing. That's where we are. The work you've seen has not yet been published. We're just getting it together now. It's just too much fun. And it's sort of a whole new generation in our lab interested in these questions of existence conditions. I certainly hope that some of the physicists here are looking for really interesting biology will turn in the direction of phage. As I said, you start out the world's most abundant organisms. What can be a better opening line for a paper? And they're tremendous questions that are not known and particularly for field ecologists to get out there and actually ask in the Adriatic where in the open ocean, you get 10 to the sixth phage per mil on average. If you take a shower, you'll be fine. How are those phage maintained? Obviously they're growing on the bacteria there. Are they limiting the density of bacteria? What is their role? I mean, I think these are really delicious questions that we haven't answered. And if we're interested in now until the microbiome, what is it doing with respect to the microbiome? What are these phage doing? Are they having any effect on this? You see, when microbiome gets away from molecular sociology, then people will start asking these kinds of questions. And what was really nice about this meeting is it was getting away from molecular sociology of who lives with who. But then there's all these mechanistic questions. And what are the phage doing in this? And I hope people are adequately interested. Thank you.