 We are back on YouTube and I'm waiting all the participants to get back from the breakout rooms and then we can start. Okay, great. I think everybody's back. So let me welcome again Joshua Weidz who is giving the second of three lectures today. So please, again, if you have questions, you can use the raise hand button or ask the question in the chat. And if you're following from YouTube, you can ask questions in the chat of YouTube. So with that, thanks again, Joshua, for being with us. And... Okay, thank you, Jacobo. I have a different audio today. I don't know if it's okay. Can you hear me? Yes, yes, I can hear you well. Good, and hopefully that also works. Yes. Yes, it does. Great. Okay, well, welcome back everyone for the second lecture after also your tutorial this morning and the second lecture in this three-part series that I'll be providing as part of this course on virus micro-dynamics and focusing on, as I mentioned yesterday on principles, ecology and therapeutics. And in order to get some continuity, I will do a much briefer introduction where each one of these is meant to be self-contained but obviously abbreviate what I covered yesterday and then go into new material. So just to give folks, again, a context, what I tried to do yesterday was to explain principles of how to think about virus micro-dynamics through this predator prey lens and take that forward, not just at the level of the individual cell but think about the consequences of how a viral infection of a bacteria, a micro might lead to the death of that individual cell but not necessarily the death of the population and how that could lead to novel changes in eco-evolutionary dynamics. What I will try to aim at today is to think more broadly about the fates of these cells and how that too can change population, evolutionary dynamics, individual ecosystem dynamics. So that's still ongoing work. And then on Thursday, I will get to the application side focusing at least on one application, that of bacteriophage therapy. And again, I'm going to try to mix theory modeling throughout and allude to certain pieces of theory. If some of this is covered in my book, some of it goes well beyond the book and you can go to the primary source material for reference. Okay, so just to make sure folks have the sort of arc in mind, you have a sense already that virus host interactions modify the fate of cells on the time scale similar to division times, but that doesn't necessarily mean the death of the population I've shown and I'll review just very briefly today, how infection and license can lead to lockable ptero-like dynamics at the population scale and obviously new dynamics as well. And then these sorts of processes iterated again and again, whether it's in a microbiome or the global oceans can have potentially large scale ecosystem effects. And just to remind folks that viruses are embedded and virus micro dynamics are embedded as part of complex ecosystems. So the death of, for example, an autotrope or a heterotrope means that those microbes aren't necessarily consumed by grazers, which would allow that organic material to go up to higher trophic levels, but instead are redirected in what is called a viral shunt back into the dissolved organic and particular organic pools where they can then be retaken up. In other words, shunting organic material back into the microbial loop and keeping organic matter small. So obviously when this starts to happen and is already described with hundreds of millions potentially of bacteria per mil, often tens of millions per mil is a typical level then that obviously is going to compound over time. But do viruses of microbes, I've been focusing a lot on this lytic wrap in the oceans and elsewhere, do more than just kill or prepare to kill? Are they doing other things? Of course, the answer is yes and I'll really focus today on this alternative pathway. So this talks premise and really the lecture here and the large body of work that we're trying to work on starts with what I would say is it seems to be a simple question, what is a virus? And when you think about a virus I already gave some examples yesterday. You often think about the charismatic version. Again, if I had said SARS-CoV-2 you would imagine this particular coronal like virus particle, here's this virus particle. But I've given some other alternative answers here. This is what is termed a lysogen in which the viral genetic material is integrated and here inside the genetic material of that of the microbial host could also be extrachromously and still passed on. And there can be other alternatives including litically infected cells. We're here, we have viruses, but now they're inside cells rather than outside cells. So in some basic sense, although we often whenever we're ascribing the word virus we use it really about this virus particle. This particle isn't necessarily the thing under selection. I would argue that this entire set ABC all of the above are what constitute a virus. And I'll try to get through in today's talk thinking about viral fitness across the entire viral life cycle whether it's inside or outside hosts and thinking about viruses in a different way can really lead to new challenges for theory experiments and field work. So I'm gonna try to get towards that vista offering a different perspective which is much more of the parasite host perspective in three parts. I'm gonna again ground ourselves in these little models via a very brief recap of what I did yesterday and then spend the bulk of time in parts two and three talking about mechanisms and patterns having to do with the cellular level mechanism of lysogeny and lysis and how that relates to potential patterns and then try to explain how we might understand the benefits of lysogeny and strategies that include this alternative pathway in which the viral genome is integrated into the host instead of killing the host that it's infected and releasing new virus particles. Okay, so let me just do this brief recap and hopefully this will reinforce what I described yesterday. Again, as you recall, we have these bacterial viruses that are diffusing randomly come in contact with cells injecting their genetic material into the cell taking over the cellular machinery having a self-assembly process and eventually these new virus particles are released. And as I described already, this is the basis for these essentially lockable terra-like models of virus micro-dynamics in which the death of the host cell does not necessarily mean the death of the population. And just to remind folks I will be using similar models today. Here I have a simplified system of resources cells and viruses where media is coming in resources cells and viruses are leaving the cells take up nutrients and then lead to new cellular biomass and new cells. These are then infected. And then with a birth size beta new virus particles are released and I've already explained how that can lead to these counterclockwise cycles where we have a large number of available host many viruses which drive down cell densities leading to decay and viral densities leading to recovery of cell densities and so on. And we get these lockable terra-like cycles which we can then see in experimental work. And in this experiment as I already explained this is about 10 days between phage T-40 coli B we get these large scale endogenous oscillations despite the fact that this is a chemist that experiment without any variability in the resource supply. So again, the viral lysis isn't leading to the death of the population brother oscillations and over a longer time scales, there can be evolution. And you can see here, as I explained the other day there can be things like cryptic dynamics and the cryptic dynamics are a result of the fact that hosts are evolved. So I went through this yesterday and just trying to refresh everyone with the basis for what is often the canonical predator prey view of virus microband. And so this means in general as I described yesterday and I won't go through all the details so this is the brief recap which is that in the absence of evolution we have a notion that virus micro-dynamics should expect to lead to this pattern at the population scale of counterclockwise cycle which we've seen, but when there's evolution in place we can get anti-phase or cryptic cycles where you can see the system seems to double back on itself and I'll just give a note for those who are somewhat new to nonlinear dynamics this implies that this system must not be two dimensional because we can't have it go in two directions via the same place in phase space so we must be missing some feature of the system and here of course that's evolution we're taking this three dimensional system and projecting it down into 2D and in a co-evolutionary case there actually can be clockwise cycle as I went over on Monday. So the takeaway here for the purposes of today's lecture is that population dynamic patterns have been used to infer putative mechanisms meaning seeing these cryptic cycles whether it's in prior prey systems or virus micro-systems usually imputes the fact that evolution is going on at the same time scale as these population dynamics but can we take this same approach more generally to non-lidic interactions so I spent a lot of time on Monday on these lidic interactions let's change our perspective and think about non-lidic interactions, okay? So now that I just did that brief recap and I don't know if I should pause, Jacobo that was really meant as kind of an introduction and summary of what I did on Monday I don't know if there are any questions that I've already popped up or I can go. In the chat, so if anyone wants to ask a question please raise your hand. That's fine, I can keep going if there are more. There is one by Pablo. Yep. Yeah, super quickly. You've said sometimes endogenous oscillations could you clarify what that is? What do endogenous mean? Sure, I'm trying to use the word endogenous E-N-D-O versus exogenous E-X-O to imply that the oscillations are arising because of feedback in the system not because I'm driving the system with some external oscillator, right? So that's what I mean that those were driving with a constant input of resources yet the response is oscillatory. Thank you. Good, okay. So let me now talk and expand our view of these virus micro systems by looking at alternative outcomes of cellular level infection. To do that I have to expand our view of the fate of this infected cell which I've said a few times we have this infection and then soon after the injection of genetic material this can lead to the death of this cell and the release of new virus particles. That's called the Lytic Pathway. But for certain phage specifically that are called temperate phage there's an alternative pathway in which the genetic materials integrated into the chromosome of the bacteria as the bacteria divide then the daughter cells also have the viral genetic material and this integrated form is called a prophage and later either by chance or through sometimes a sensing process related to stress or other features this prophage can be induced re-initiating the Lytic Pathway. The key point here is that in this pathway the Lytic Pathway the virus leads to the death of the cell from the release of new virus particles and the other there's not a death of the cell and in fact even though the virus has gotten or obtained or found this bacterial cell it is not actively killing it at least not yet. And this study of lysogeny is also quite old and dates back to really the origins of thinking about both molecular biology and gene regulation but also in terms of basic virus micro dynamics. This study has been revitalized in many ways there's a beautiful book by Petashina Genetic Switch focusing on phage lambda in particular and a number of studies in the past that say 15 years or so really have leveraged new techniques to label and look at these same problems not in the population scale but at these individual cell or phage levels and here's an example from the work of Edel Golding in which they have these labeled phage so the capsids are labeled and you can actually see singly infected or absorbing cells or those in which there are more than one phage absorbing and infecting an individual cell but they've labeled the system as this capsid with green but also included a promoter that will express this red fluorescent reporter in so far as the lysogeny pathway is an issue. So what you can see is that some of the cells and it's not actually a coincidence that this multiply infected cell ends up expressing red because that tends to be the case but you can see that some of the cells express this red and some as you can see here are producing new phage and then they've burst and released new progeny phage whereas others as you can see divide inherit the property of the mother cell. What's interesting is that these are not just stochastic outcomes there is elements of stochasticity but they're also driven in part by the state of the system. So for example, the viral concentration we're thinking about it in the single cell level as the multiplicity of infection the probability of lysogeny actually goes up. So counterintuitively maybe if a cell is infected by more viruses this would seem to lead to a more virulent outcome. Would you rather have a large or small dose of a particular infection? You'd probably prefer a small dose and imagine that the outcome will be less virulent for temperate phage lambda and this happens in a number of circumstances the outcomes are less virulent the more multiple infection the more phage are infecting the same cell. So here you can see the probability of lysogeny this option here in which the cell is not lys goes up as a function of the multiplicity infection from here you have one to about 20% to something like 80%. So it's not deterministic it's not zero or one but it actually changes as a function of this multiplicity of infection. And this actually goes back to wonderful work by Philipp Kurilski in the early 1970s and just as there is this probabilistic decision which is driven by some ecological dynamics so to the induction probability also depends on stress in this nice way depending on the UV dose there's a much higher chance of being induced whereas depending on the other dose only a smaller fraction will be induced. So you can see here that we have these life history traits associated with the fate of individual cells they can vary and that also can lead to certain feedbacks in the system. Okay, that is the how question. In other words, there's a whole field built around how this works. How does a phage have these alternative outcomes and today's lecture is not focused on this how question and you can read more in potassium for it and recent work by the Golden Group, our group many other groups have been trying to address this how question which has to do with gene regulation but today I wanna focus on the why question. Why be tempered? Why not if this is a virus that's acting like a predator the simple predator there's a cell why not take advantage of this opportunity to kill it and release many new virus particles? So Frank Stewart and Bruce Levin in a wonderful paper back in the mid-80s asked this question of why be tempered? And to do so, they also use simple couple nonlinear dynamic models of the kind that you're hearing about in your tutorials also I've introduced here which describe in some sense what happens to cells and to viruses with time. And I'll elaborate on a sort of modern version of these same models but their premise was one that they called this feast or famine hypothesis that tempered phage would presumably do better when few hosts are available and extra cellular mortality is high. In other words, it would seem in order to explain this phenomenon that phage can not to kill is that if there's very few hosts left if a phage got in and killed that host then there would be no host left for its progeny to infect. A, that is a bit of group or even multi-level selection. If it's in the advantage of the virus to do it why doesn't it just do it? And also they were never able to obtain solutions consistent with it. It was a nice hypothesis but it was hard to actually figure out a solution for it. So they would introduce these exogenous oscillations but there didn't seem to a way to actually make a kind of proof or demonstration that this was in fact the evolution rationale for why to be tempered. This is not just a question and let me just hold here for a moment. This is also consistent with a lot of the phage Lambda work in the sense that if multiple phage are infecting the same host that also indicates that are probably not many uninfected hosts left. And so again, it seems with this Feast or Famine hypothesis that at that point hosts may be relatively non-abundant and if they were to be killed because that was where the temperate strategy seemed to go that would imply that maybe the host would go away but that's not what we find. We find the opposite. This is not just a question of phage Lambda but it also became the paradigm in marine systems which is known through this moniker of the seasonal time bombs. In other words, lysogen is prevalent given low productivity and lysis is elevated high productivity. You can see this here in the study looking at the fraction of infected cells during essentially low productive periods and high productive periods. And also shown here is the fraction of bacteria that are lysogens and they can figure this out by trying to induce them through a inducing agent for example, Minomycin C. And what you can see is that low productive periods there are very few visibly infected cells whereas in the high productive, high density environments and I wanna make sure that we separate those two concepts there seems to be a lot of visibly infected cells. And likewise, there seems to be a switch in which there seem to be many lysogens. In other words, phage that are integrated but not actively infecting or producing viruses in the low productive periods and very few in the high productive periods, okay? And this became certainly a dogma for many years until a few years ago when an alternative hypothesis was introduced and that is called piggyback the winner which is literally the opposite of what I just described to. And this is that lysogeny should be positively correlated with increases in host density and productivity. In other words, as there are more bacteria and things get more productive there should be more lysogeny and less lysos. And the opposite, which is again the opposite of the phage lambda story and the steward and leaven hypothesis when there are fewer cells and less productive environments there should be more lysos. And this was meant in part to explain patterns between virus like particles, viruses and microbes in ocean systems. This is one particular example where you have viruses on the y-axis, microbes, bacteria largely on the x-axis, log scale. So we have a straight line here which denotes a linear relationship and the data although scattered implies a slope that is less than one. In other words, the ratio of virus to microbes seems to decrease as microbes increase. So that was a claim and this was the putative mechanism. So now let me try to disentangle those two claims. First of all, the idea that there is a fixed ratio between virus and microbes which you'll often see in the literature and you'll often see it as described as 10 to one is just not the case. It is a decent median but we in a totally independent study and there's even a third group who did something around the same time looked at this question and found that here are all these individual relationships by study and what you can see is that the best fit for the entire data is a parallel law with an exponent less than one implying exactly that the ratio of virus to microbes decreases as microbes increase but it can be offset. You can have higher numbers, you can have lower numbers but certainly it seems as if this pattern holds on the abundant side but the challenge is whether or not this idea is enough to explain that pattern meaning it's one thing to have the model explain the pattern but the question is it unique can many models explain that same pattern? In the piggyback the winner model they used again these system of nonlinear differential equations of microbes and viruses but notably no lysogens. Instead what they had is that the that the viral efficiency so here you have lysis and the viral efficiency scaled with N over K so even though the idea is that activity of lysis activity goes down in fact their model has it going up. So here you can see this is a standard model but it goes the other way. It's true that if you look at the outcome of the model it finds this pattern and this is the result of our re-analysis of this work but it is also true if you just vary parameters because of parameter entanglement in the steady state outcomes you can also get this feature that the virus microbe ratio virus microbe ratio goes down as microbial density goes up and you don't need to invoke this mechanism in order to see the same relations. So that implies that this pattern alone may be insufficient to make the claim that this is a piggyback the winter mechanism. However, they then look directly at metagenomic evidence and tried to see in the viral fraction so those are virus particles outside cells what fraction of them had things indicative of pro-virus like reads in other words indicating that there may be the possibility of being temperate and claim that this went up which is what their hypothesis is. This is our re-analysis of this data and as you can see, there's not much of a relationship in the pro-virus like reads in the integrases this is and the excision ages all these are hallmarks of being temperate and in our view, neither the metagenomics nor the abundance data support directly this evidence of piggyback the winter but notably it doesn't go down either. So there seems to be an absence of evidence for a particular relationship. Nonetheless, this idea that one can go from a pattern to a mechanism is enticing and in fact, the following year, a separate study concluded that the findings of a decline of a ratio of viruses to microbes here I'm showing again virus to microbe ratio microbes you'll notice again and again in this separate metagenomics study of linking viruses to hosts that it seems like this pattern is ubiquitous and because that was claimed to be a proof of piggyback the winter they say it corroborates the proposed theory. Having already worked in the space a little bit I saw this paper and was a bit concerned. And again, maybe we're together I would ask to see if you were concerned but you'll notice that these lines which denote virus microbe abundances or metagenomic inferred abundance for different virus host pairs all seem to have parallel slips. I hope that's clear. And if you can look at it you'll see that if we started about negative two to two something about this would be a slope of negative one and I was worried that these parallel slopes all looked a bit too much like negative one. Here is our replot of the same data with a negative one slope as a guide to your eye and you can understand that this Y axis is not something independent but it's a ratio of virus to microbes plotted against microbes. In other words, this is a plot of Y over X versus X but if Y over X goes like X to the minus one this implies that if we just look at the virus abundance to the host abundance you can see that almost all of these lines are statistically not significantly different than zero. In other words, an absence of a slope which means that it appears to be unrelated to host abundances or at least we don't have the evidence say they're related and frankly that's a counter indicator for piggyback the winner which implies viruses are going up in density as hosts go up in density just not as quickly which is why the ratio goes down. So again, the takeaway here is that we feel there's an absence of evidence for positive correlation whether you're looking at misogyny proxies or examining ratio of virus to microbes as a proxy but it does raise some interesting questions because we don't see the opposite relationship. We're not seeing the sort of inverse relationship as one might expect. So I'll try now in this third part to provide some thoughts about how we might think about the benefits of misogyny and when we might expect to see more or less of that strategy, both in experimental systems and natural systems and now it's probably a good holding point. Let me get one thing before I... My clock was on the wrong side of the room. So yes, so if there is any question, please. Okay, there is a question from Ronaldo, please. Yes, hi, can you hear me? Yep. Okay, thank you. Thank you, professor. This is a very interesting lecture. I was just curious about what are the mechanisms that trigger lysis from lysogenic? You said that stress and sensing could be factors but I was just curious if you could give some examples on when do cells with the viral genome included in their own genome start the lytic cycle? Right, so there is a regulatory mechanism that keeps a prophage stably integrated inside a cell and it's true that we know about some of these largely from a few model systems. So I'm sure there are many things left to discover but the idea is that, for example, if there is DNA damage to the cell, then there's a repair mechanism that is going to be activated. It turns out that the repressor system which keeps the prophage stably integrated can then those repressor proteins can then be cleaved by the same DNA repair mechanism which then leads to an induction event. So a typical way to think about natural systems is DNA damage, some sort of damage agent or stress, whether it's UV or mitomycin C are all experimentally standard ways to induce because you're leveraging this sort of evolved system. There may be other mechanisms when we think about the way out, there are really two decision switches there, in and out and going in, there's all sorts of interesting questions to be raised which I didn't go into today on the how side because if we have multiple phages that are affecting the same cell, in some ways we have a gene dosage question that we need to ask because now you have more copies of this phage genome and you might think, well, how would that change in outcome? But these are systems with nonlinear feedback so if we're increasing the rates of everything but there's a nonlinear feedback, we can actually preferentially end up in one kind of fate rather than the other. But from the induction side, there's also a switch. And again, as I said, that is controlled by a coupling between the regulatory mechanism, for example, the C1 repressor and the status of the DNA repair enzymes and those two together can lead to induction. There may also be queues into quorum sensing and there are other systems too, for example, the Arbitrium system which is quite interesting from the SOREC group and that has its own mechanisms of integrating in those decision switches. So I think as we begin to see more of these model systems we'll have more of these examples. Okay, thank you. Thank you very much. Great, any other question? Oh, yes, there is a question by Ravi, please. Hi, just a quick question. Are there any fitness costs while the virus is inside, the phage is inside the before lysis? Are there physiological costs to the bacteria or anything like that? So I will be talking about some of the ways in which there could be fitness benefits and fitness costs, right? Because certainly a fitness benefit, if the virus brings with it a gene that is somehow beneficial, then in fact, there's an entanglement and the reproduction of the cell is also reproducing the virus and it's sort of their mutual interest. And I will talk about that next. There could be costs, though it seems given the size of bacterial genomes and viral genomes relatively speaking that replication costs may be small but there may be other costs with respect to the expression of repressor proteins, there may be other costs that they're bringing in genes that are not beneficial, right? So there can be all sorts of ways. I'll talk more about that in the next section. Yeah, sounds good, thank you. Great, there is another question by Mites. Yes, hi Joshua, just a clarification. So basically that last slide that you showed us, what I understood is that virus abundance is essentially invariant to the abundance of host. In this particular, and let me clarify, in this particular study which tried to use a metagenomic based approach. Right, okay. If we look at direct particle counts and microbial particle counts at the population level, the community level, excuse me, then we see a positive relationship. Yes, sub one. Okay, thank you. Yep, should I continue? Yes, I think. Okay, good. And I think I'm still on track on time, so it was looking good. So let me go back and ask this question again because despite the disagreement and some of the debate, and I wanna point out that debate in science is usually a good thing, right? We're trying to clarify ideas and we have an intent, a shared intent to try to increase our own understanding, shedding light on complicated, hard problems. And so I think this question of what environmental conditions should favor lisage rather than licenses is a good one. And I can imagine there are circumstances in which there may not be one monolithic answer to this question, but nonetheless, I'm going to try at least build a conceptual foundation for how we could begin to address it. And I'll try to do this by making an analogy, and I realize this is a very international group. So in English, this is saying a bird in the hand is worth two in the bush, which I will try to translate because certain times sayings may not always be immediately understandable. I hope you get the idea that you have something, it's in your hand, and you might be willing to trade it for something uncertain because it's out there. But if you're going to do that, you better get more because those things are uncertain. I'm not going to trade my bird in the hand for one in the bush. I should get at least two. And certain cultures have similar sayings. I was told in Spain, there's a similar saying, but a bird in the hand is worth 100 in the bush or something similar. So you can tell me about uncertainty in cultures and the number of the trade that you have to make. But I will try to make a new puzzle here that a virus is in the cell. And it's worth N in the bloom, meaning the virus is inside the cell and you can put out all these virus particles, but what is N? And also how many cells is it or need to be out there and how uncertain does the situation have to be for it to be worth giving up the cell that you've found, that the virus has found and then going back out into the environment, this uncertain environment, okay? So to do this, I'm going to move away for a moment from the population view and take an individual view. And again, I've already described this notion of this encounter and I'm going to use and anchor our thinking in terms of a lytic cycle in which we start with the virus that injects its genetic material into the host, but I'm going to call this the mother virus. It lices leading potentially to hundreds of virus particles, but I will claim that this is not the fitness that we should talk about because many of these, if not most of these virus particles, maybe they're defective, they don't ever find a host, only a very few in this example, three end up infecting a new host and we'll call these progeny viruses. And I would call the fitness at the individual level here as our HOR for horizontal as three. And in contrast, if I think about temperate phage, yes, they can do this, but they might instead integrate in my ask question, well, why? There's no production of viruses. Viruses are these particles. How can you have fitness? And how do I account for the fact that a strategy is avoiding making itself, right? This virus particle, if that's what we think of viruses, but instead, if I think about the life cycle as being under selection, then here we have a mother virus. It divides three times. Each of these have their own fitness. These, we can arbitrarily call these daughter viruses as progeny and eventually the cell dies. So here by initiating misogyny, I would say that the fitness at the individual level of this virus is three. Three new progeny viruses. And I've called this VER for vertical and yet no virus particles were produced. My point here is that it seems that two vastly different strategies can have the same fitness at the individual level. I put that in quotes for intentional reasons. And how does this depend on cell densities on the environment? Cause we want to connect this back to the ecological context, okay? So let's go revisit this population dynamics of lytic viruses. I've given you this individual perspective, but we can think about the population perspective as having a population of susceptibles, infected and virus particles, susceptible cells grow logistically. They're infected, lead to new infected cells, which over a time period, one over eight of this latent period lead to a lytic event. All of these things may die or decay. And we could get essentially conditions by which a susceptible population may be infectable by a virus such that the viruses increase in abundance and proliferate. And this is nothing other than looking, again, as I mentioned before, about essentially searching for a positive eigenvalue of this otherwise is stable system, the absence of viruses, but unstable given a small introduction of viruses. And you can see here, viruses should increase in population within these cells, using exclusively horizontal transmission only through the lytic pathway, whenever this criteria is met. And again, I don't wanna delay my interpretation. I've chosen this calligraphic R because I mean, intentionally to evoke this notion of a basic reproduction number. And now, since everyone is an armchair epidemiologist, some of us are actually doing this kind of stuff, but you will obviously recognize what I mean by that and why the condition is greater than one. And let me unpack this. Let's take the perspective of an infected cell. An infected cell will lice eta over eta plus D prime of the time because it could either die via some other mechanism or through viral lysis. So a fraction of an infected cell, a fraction of time will lead to a burst event producing beta viruses. Of these only a fraction will infect cells, which as you can see depends on cell densities. Alternatively, I could start with a virus particle and starting with a virus particle, ask how many virus particles are produced in this life cycle. Well, a fraction of those virus particles, right denoted here, we'll find cells, of those a fraction is infected cells will burst times the number of new virus particles produced. And either way, when I think of a life cycle from in a cell sense or in a virus particle sense, I get the same number. And again, I've written it here out in words. When this is greater than one, we have the increase of this virus population. Notably though, it is not inevitable. It depends on the susceptible population. Because as you can see here, the chance of actually finding a host is going to saturate as we increase susceptible populations, obviously go down as we have fewer cells. So if we have a fixed burst size, it means that you have to have a sufficient number of susceptible cells for there to be invasion. And here I've written out the are not criteria. Here's this break point. And below this point, this virus will be unable to invade, even if it has a very high burst size. Again, showing you that it's not just about how well the cell, the virus exploits the cell, but the ecological context. And clearly in all of these cases, as we add more cells, this seems to be enabling a larger state space of potential invasion scenarios for this horizontally transmitted virus. So the takeaway here is that ecological conditions with more susceptible cells and viral trace with more efficient infections favor this lytic antagonistic moment. Let's now do the same thing for latent viruses, including temperate phage and focusing again, only on this exclusive route in terms of our calculation. But here we have susceptible cells, lysogens, which can also divide. And I'll just note that N is S plus L. So it's the total number of cells in the system. And here we have infection, but some of these cells may lyse and this fraction P and another fraction Q may be dividing. And when there's a lysis event, we get production of new virus particles. I'm going to focus on the case where P is zero. Just look at this exclusive growth via lysogeny and ask the question, how can viruses increase and proliferate this population? They can do so using exclusively vertical transmission when this number is greater than one. And we can think of this as essentially the average number of new lysogens produced given one lysogen in the population. And to do that, we see that the lysogens will persist on average one over D prime, which is why we have this one over D prime. And they will have a division rate B prime and it'll modulated by density. So if we have a rare lysogen and the susceptible cells are high abundance relative to their carrying capacity, it will be very hard to proliferate. So you can see this is in essence, division rate times cell lifespan. What this also implies, and this goes back to a question that was anticipated near the end of the second part, is that the benefits or costs, the direct benefits or costs are gonna modulate the conditions by which this vertical transmission pathways could be favored. When the susceptible population is relatively low compared to this carrying capacity, then you can see depending on the benefits, this B prime relative to B, if there are high benefits and even low fitness benefits, there's a large regime in which this rare lysogen can proliferate. But when there are fitness costs, well, it doesn't ever seem to be good. It can't ever do it alone. Notably that irrespective of the fitness benefit or costs, you can see that this R not level is going down so there can be a transition depending on the level of fitness benefits at which point low densities are actually more likely to yield the proliferation of a lysogen rather than high density. So now we're getting some direct evidence rather than having to appeal to this idea that they should not kill their hosts because that would be bad for them in the future, but rather saying it's good for them now. As you can see here, if these viruses were to try to kill these hosts at low host densities, this is not a viable strategy. Whereas it can be a viable strategy to forego killing a host and proliferate along with it as a profige. So the takeaway here is ecological conditions with the reduced niche competition, direct cell benefits or lower and survivorship can favor latent strategies. We can even start to do intermediate cases. There are not just these dichotomous outcomes but also other forms of infections including chronic infections. And most notably this is through filamentous phage which bud rather than burst in which case these infected cells are dividing but you'll notice that there's a production rate of viruses from infected cells and that doesn't include the death of the cell. And here in my individual example, you'll see that this cell divides once but buds twice, it has more than two budding viruses but two of these budding viruses infect horizontally. So we have a basic reproduction which is the sum of the horizontal and vertical components. And so when we actually do the analysis in full we identify precisely the sum for the reasons I've just explained that we have this vertical average number of new infected cells vertically and here there's an average duration during which there's alpha new viruses produced and there's a fraction of them that find new cells. So we have the same rationale. When we put all of this together you can see that these intermediate cases although this is a chronic mode I'll go explain the temperate version in a moment can end up being invasible across the entire spectrum of densities where these dichotomous outcomes will eventually fail out these other extremes. This particular case we have the highest basic reproduction number in the middle but I wanna point out that that is not Malthusian fitness so we have to think carefully about feedbacks which is what I'm gonna start talking about in a moment. Okay, so let me just do this takeaway and then maybe there'll be a few questions before I get to the final part here just to say that again that these temperate or chronic modes can be favored when susceptible populations are low. So now we have really beginnings of answers to why be temperate because on the other hand this virulent strategy is not just that it's bad for the host population it's bad for the virus. It's not evolutionary beneficial to kill the host because you simply don't propagate there are not enough susceptible cells in order to produce more than one infected cell on average and this means that this range in which this non-horizontal mode is favored could be much greater range than we have expected and suggest that we might find this in far more cases than we've thought about before. So to answer this question I think it requires a unified metric at least to answer the question of invasion the long-term question remains open and a challenge for the field thinking about virus host dynamics if we wanna understand integration I think we have to go beyond the predator-prey dynamic because you can't account for it there's not an apples-to-apples way to compare but if you use this epidemiological notion and think about this parasite host infection as transmitting horizontally or vertically we do have a unified way that we can compare temperate strategies with these litic or virulent strategies, okay. So I should pause there before I do a few more slides and wrap up. Okay, so there are a few questions from the chat so perhaps I can start reading them. So the first one is from Egar and is the following is there any impact of microbial viral co-evolution to the disogyny level of the page and is there any benefit for the microbes to keep the viral gene kept integrated to their genome? Right, so yes there is co-evolution there's been very limited work on the evolution in the lab of lysogyny in the next stage I'm gonna talk about some of this within temperate phase and also to point out that one of the benefits of having a prophage not only can there be the shift of genes though of course the danger for the virus if it doesn't get out is that it's under most of the genome is under neutral selection which then can drift away into inactivity but also an active prophage can protect a I don't think that's my computer can protect a host against infection by certain kinds of viruses so it's not universally protected but there can be things like super immunity and in other words it helps protect the virus from the bacteria from infection by the virus that is a benefit. Great, there is a second question and these are the progenies from leaky cycles identical because obviously the progenies from lysogyny would undergo several mutations especially as they cause plasmid degeneration. Well, people have asked this question is there are any two snowflakes the same? Each one is a little bit different I think it's a fair question about viruses both in terms of their assembly obviously they're gonna be slightly different but in terms of their genome you can do the math and you ask the question with something about 50,000 base pairs and an error rate that's typical for double stranded viruses I imagine that maybe some of them have precisely the same genome but many might not and so the Linux cycle and I have to think through that a little bit more carefully I wanna be careful about whether or not I really believe that oh, let me think more about that whether I think that they're on average you expect differences you probably do but remember that there is an error correction mechanism so if it's going through a few generations we can ask the question is that gonna be any different than maybe a slightly higher rate in the replication cycle during lysis but yes, you do expect that the progeny are slightly different and that's the grist for evolution that can happen for the virus both because of the accumulation during the integrated phase but also in the event of the induction during the lidic production phase Great, there is one last question which I think is gonna be short so is there any assessment on many of the phages are temperate? Are what? How many are temperate? How many are temperate? Being, if we go out to a natural system and we were to ask the question is that virus that we've identified have the ability to be temperate? Is that the question in some sense? Yeah, I don't think we have a great answer to that that's in fact the interest of a number of groups it's hard right now to figure out in some sense the potential or conditions where something may be temperate there are certain hallmark genes people have been working on this the past few years of looking for omics based methods to identify hallmark genes associated with lysology doesn't mean that that's going to be fulfilled in a particular system there may be other mechanisms so I think we probably have an undercount and it's probably more ubiquitous than we expect but I don't have a fraction that I can say that fraction of natural systems is absolutely temperate and the other fraction is not in the absence of integration excisionase are probably good sign but we're again still looking for the things we know I don't have a good number yet as a firm estimate Great, so there are no other questions So let me just wrap up here I only have a few more slides left Okay, so the problem when we I've given this notion of this initial invasion the problem though going back in time is that the models are actually quite different Frank Stewart and Bruce Levin's model included resources but didn't include an explicit infected state there's another model which I'll talk about which has lysogens but again doesn't include some of the other features like resources we've built these more complicated models in which there's an active switch between lysogyny and this active state and an active state of induction with or without resources so it gets to be a little bit confusing with respect to whether or not these findings hold and this means that you really have very different model structures or what appear to be different model structures and how much of what we just found transcends these details I will just point out that we think that this does transcend details and in a paper that just came out a few months ago who knows how many months ago it was because this year has been very long so I've lost all track of time we have found the same structure for R naught here for all of these models and I've shown a diagrammatic view which I know this looks crazy but we actually can use this to calculate and I'll just point out that the basic reproduction all of these models can be written this diagrammatic form where we have essentially loops which are a lytic loop, a lysogenic loop or what we call a lysolytic loop but notably the form involves things with a square root which I will also note have been observed before algebraically because you get these conditions and are noted as complicated what we've interpreted these as the first generation and second generation loops and because R naught is the average number of infected cells produced in a generation here when we take the second generation we have to discount them by a square root because we're essentially multiplying these together I'll also note that it gets discounted by impossible second generation loops where we hop from one lysogenic loop to the lytic loop it turns out that when we actually want to calculate these things we can use this formula but of course the values here are simply the basic reproduction number of these horizontal and vertical loops and those will depend on the model details but the qualitative form is precisely the same okay so you can write crazy formulas I won't make you just to point out that you can actually do this for all these models but they all reduce even though the algebra is complicated the same fundamental form and what this means is that we end up getting the same kind of answers whether we look at the implicit model of infection with the explicit model and the takeaway point is that when profage provide a benefit to cellular growth what we see is that this vertical strategy is always good when they impose a cost it always seems to be bad the horizontal strategy obviously gets better as there are more hosts available and there are intermediate strategies as I mentioned before that can get the kind of best of both worlds and have a positive invasion fitness irrespective of cell density but we still raise this question what happens here at low cell densities because it seems like then we could have a problem where there are regimes in which none of these strategies seem to work as you notice here none of them seem to be invasible and just to point out different model structures some quantitative differences but qualitatively the same answers to think about this really does require a long-term framework and I know I'm at the end of my time just to point out that Berngruber and Gendon in a beautiful paper from 2013 analyzed this by looking at the ratio of these virulent and non-virulent types showing that there was evolution happening in terms of these strategies at the time scale of the epidemic so that you have changes in the ratios just like I alluded to in my first lecture at the time scale of invasion but let me try to unpack it here in a different way what we've done here in this simulation is ask the question can temperate viruses that impose a direct fitness cost invade a system in the event that they have an indirect or ecological context benefit which is they provide immunity to infection by litic viruses so they hurt the host in terms of growth but help in terms of immunity what we see is that when we start the system hear our cells, here's the resources we add these tempered viruses they go away they can't invade there's many hosts that are available but actually this favors the rare type that imposes the cost on growth but this is an ideal time for litic viruses to invade so if we add them at some low densities they immediately shoot up reducing cellular densities and now we re-add the very same tempered virus that we tried to add before that failed it can invade it's competing with fewer cells and also it's protecting those cells that are infected from infection and lysis and what we find is that depending on the probability of lysogeny these different colors denote the degree of immunity no benefits and complete protection from infection we see that as long as there's some benefit of infection we have a temper phase that can invade when it's invading not a fully naive population but one in which litic virus already there which implies that in some sense litic viruses can help tempered viruses invade even if they impose a fitness cost in a growth sense but not insofar as they provide some contextual benefit what I hope to take away from this is to say that if we wanna think about the long term we're gonna have to think about coexistence not just of viruses and hosts but of different kinds of viral strategies and there may be cases where in fact these litic virus strategies make a template and restructure or reshape the environment so that tempered and litic or virulent strategy can coexist together. So to close and I think I'm just at time what is a virus? I would argue it's really all of the above that we should be thinking about viral fitness across the entire viral life cycle and in doing so I hope that we get some new ideas not just for theory but also for ways to probe invasion and experiments and interpret including really at these marine systems we're finding more evidence of non-litic infections and trying to understand both when they arise how they interact with these litic infections how ubiquitous they are these remain truly open questions for the field. And with that just to point out a lot of this has come out in the past few years goes well beyond what is described in this book and I've given you just a few examples of ongoing work and happy to take some questions before you go into your break. Great so thanks Joshua for the fantastic talk so if there is any question please write it in the chat or raise your hand, any question? We took a number during the talk. So I think it's fine that we, if there is no, okay so I think we can stop here and Joshua Oh there is a question, okay. So please go ahead with the question Monday. Please if you want to ask the question Monday. I think you are muted Monday. Maybe you can type the question into the chat because we can't hear you or you can write to me afterwards I think we're having a technical difficulties Yes, okay so Joshua will be with us in two days from now So if you have questions you can also ask today after tomorrow so thank you again everybody so we'll resume tomorrow at the same time as today, okay So keep in mind to all