 The next lecture is Joshua Weitz, who is my pleasure to introduce. So Joshua is a professor at the School of Biological Sciences and Physics at Georgia Tech in the United States. He's an interdisciplinary researcher with a very broad range of interests and perspectives in mainly theoretical ecology and quantitative biology. Most of his recent research is focused on bacteriophage interactions and dynamics at multiple scales from the fine-scale microscopic details of this interaction to the ecosystem large-scale consequences. So today Joshua Weitz is giving the first lecture of three... Sorry, there was... Can you hear me? Yes, I can hear you. I'm giving one of three lectures. Great. OK. Because I received comments in the chat. So, great. So today is giving the first of three lectures of virus micro-dynamics. So, please, Joshua, thank you very much for giving these three lectures. Please share the screen. And let me remind the audience, if you have a question, please use the raise hand button that you can find under participants of Zoom. And I'll give you the possibility to talk. OK, great. Can you hear me? Jackable. Yes, perfect. OK, wonderful. Thanks for the invitation. Welcome to the many 100 plus, not 200 plus, that are here joining internationally. I just have a few preliminary slides before I get started. First of all, just to let folks know that I'm also the founding director of a Quantitative Biosense's graduate program at Georgia Tech. We are accepting applications now for entry in fall 2021 at qbios.gatech.edu. And if you want more info, again, go to the website. We have cohorts of approximately eight folks per year looking to welcome a new cohort in the coming year. And just a bit about our group, again, we're located in the United States, the Southeast United States, the state of Georgia. And that gives you some indication of the team, folks from all over the world, much like in this meeting, to work on problems related to virus micro-dynamics and theoretical ecology, evolutionary biology, quantitative biosciences, more generally. As Jacobo mentioned, I'll be giving one of three lectures. I recognize the background here is quite broad. So I'll try to use today's lecture as an opportunity to set a foundation. It may cover more material than is humanly possible in this hour, but I will try. And if it goes too fast, I'm under the impression that, A, this is being recorded and it can be reshared. And also that the slides will be made available so you can review them at your leisure. And again, this is collaborative work and I'll try to go over a number of different topics supported by the National Science Foundation, NIH, Army Research Office, Simons Foundation and others. Okay, so to get started, I'll try to start with a boring slide visually at least. And although it looks boring to look at, I'm going to claim that this is actually a fascinating experiment. Some of you may be familiar with it. You can see here in the rows, you have these experiment numbers and these are replicated the same experiment. And as you can see, there's a lot of variability across a different experiment. And I'll just only give the hint that these have something to do with counting bacterial colonies. And if any of you have ever done experiments with bacterial growth, you would probably imagine that you don't want to report back the results of an experiment where sometimes you've got no colony, sometimes 303 and 483, totally unpredictable, okay? But yet this experiment, as I'll explain in a moment, sits at the very heart of how we think of virus microbe dynamics and in fact really influences all of modern biology. I'll give just one example of this particular experiment number five where you see this incredible variability, sometimes no colony, sometimes 100 plus, extreme variability. Now what this actually was is the number of colonies that were resistant to the action of a particular phage. And so this tells us something about the emergence of resistance in a population. And it comes from this paper that many of you know by Luria and Delbrook on mutations from susceptibility to resistance against viruses. And it comes directly here, that one that I highlighted here from experiment number 16 and Luria Delbrook along with Chase won the Nobel Prize in 1969 in large part due to the understanding and advances that they were able to push ahead using this experimental setup. Now to understand a little bit more at the time we have to go back in time and think a little bit about the differences between what people thought might be the basis for the emergence of viral resistance within bacteria. It could be dependent on selection or independent of selection really mutations more generally it was not necessarily clear which way these things work. Was it Darwinian in some sense or Lamarckian in another sense? So we can imagine for a moment as a thought experiment the growth of a bacterial population from a single ancestor where you can see these are all susceptible they're denoted as clear. They're dividing over time until after a certain number of generations log two of N the final size of the population we have this entirely susceptible population which is then exposed to viruses that should presumably infect and lice all of these bacteria except through a acquisition mechanism if resistance is dependent upon interaction with the virus in other words, selection mutations are selected are dependent on selection and the subset of these will survive our own infection but in some sense like a Poisson experiment Poisson distribution meaning there's some random chance per bacteria and if we do this again we'll get a small number repeatably a relatively small number of colonies that will have this particular phenotypic trait. Alternatively, it could be that mutations are independent rather than dependent on selection and therefore early in the proliferation process even before viruses were added a subpopulation had a mutation which were then resistant to viruses only then were revealed when you actually expose them and then a large number of these bacteria again, which already present survived our own infection and that large number really depends on how far back in time how many generations ago this mutation occurred and then proliferated. And in light of this one expects actually that in this context you should have significant variability the earlier these mutations occurred the more they may be in the final event and the later they occurred the smaller even none at all. And this is precisely revealed here where I look at the number of mutants this is a Poisson fit obviously it's not a good fit this is the number of cultures with this number of mutants and you can see this long tail effect, right? Where you can see that in some cases you get these rare jackpot light events in which there's a number of these cultures that have many mutants whereas this is just certainly not expected in the Poisson case, right? So this table that looks visually quite boring actually tells a very important Nobel Prize winning story which is that mutations are independent of selection at least in general and we can talk about Christopher Cass some other point maybe in the chat. So the takeaway from this in the early 1940s that viruses impose a strong selection pressure post mutations that confer resistance are beneficial in some fundamental sense than viruses induced host evolution, right? We have a change in the frequency of genotypes in a population that is induced by actions of this viral selection pressure. But what about the viruses? So this famous paper by Lurie and Delbrook is not often seen from the other side, right? Which is viruses are a convenient way to impose a selection pressure but what do the viruses do? In fact, in a later work Lurie explored this question by looking at the inducement of resistance amongst bacteria against phage but also then counter defense in some ways niche expansion by phage against bacteria and here the squares denote the phage, these circular oval like things denote the bacteria and what you can see through the solid lines are the intrinsic ability of this particular phage to infect in life's particular strains of bacteria and you'll notice the absence of such lines in other cases where these host range expansion mutants of phage can infect not only the ancestral types but also these newly evolved types. So in some sense, we have the host range of viruses expanding you can see here twice and then eventually in these experiments a phage resistant host range emerged. So yes, not only can bacteria induce evolution in phage and vice versa but at least in these early experiments there was an ocean of co-evolution but there was a sense that this interaction might get short circuited. In fact, really this dogma persisted for decades and this dogma is encapsulated by this idea the co-evolution potential virulent phage is less than that of the bacterial host back in the mid-80s. And part of this was also informed by the fact that it just seemed very hard to find abundant bacteria phage in natural systems. And maybe that was yet another indication that the bacteria kept escaping their phage parasites but then something happened. And what happened was a few years later in the late 80s, a group looking at aquatic systems began to take a culture independent approach to try to assay the abundance of viruses in natural systems by taking water samples here from a lake they were also doing this in marine systems and then staining anything that seemed to contain genetic material, DNA. And then if you see these arrows counting the number of these small dots because here's the scale of one micron these things seem to be about 50 nanometers to 100 nanometers in size. And there were a lot of them. And they went back through and counted how many of these virus-like particles there were in these particular systems back and for based on the dilution to the abundance of viruses and found that there were 250 million virus particles from millilayer and natural waters 1,000 to 10 million times higher than previous reports, right? So this is just an incredible difference in part of this because previous reports were using a host and almost certainly the wrong host for the bulk of these viruses as a means to count by looking for plaques in the same way that Lurie and Delbrook look but if we don't know the host and we certainly don't know the virus and we may under count. So there were since since in the late 80s and this is really the jumpstart of this new approach and a new really ecological orientation to thinking hard about virus micro dynamics in environmental systems. And it was then realized about a decade later that not only were there a lot of viruses and they could infect in lice particular bacteria but they also had a role in the ecosystem because as viruses infected in lice bacteria they could redirect organic material this is DOM dissolved organic material back into the ecosystem. So again, there was a notion not only where virus is interesting from their perspective potentially as agents of mortality but also in the role in shaping ecosystems. And you can see that here again they divert the flow of carbon and nutrients releasing the contents of cells back into this DOM pool. And of course there were a lot of viruses and part of the challenge is once you have 10 million or 100 million per milliliter these are all not the same type these are not monolithic it's not a monoculture and from the outset and this hasn't changed that much although there's been improvements in understanding viral types the vast majority of these were basically unknown to science. So the majority of these were uncharacterized much of the diversity in the early 2000s was uncharacterized and obviously that's been improved quite significantly since then. So what do we talk about when we talk about viruses? I would say in normal times we might talk about viruses that infect humans whether it's Ebola, Zika or influenza and obviously right now I'm giving and I'm aware that I am giving a lecture about virus dynamics when most people are just thinking about this, right? SARS-CoV-2 and yet I won't be talking about that today or in the next few lectures I'm looking forward to this break and talking about something else other exciting stuff that we're doing in the group but just to point out that yes over the past year we have been working on COVID-19 quite extensively as I'm sure many of you have in all sorts of ways including what you see in the upper right is some of our collective work to develop asymptomatic surveillance system at Georgia Tech which is available to anyone, students, staff, faculty on a weekly basis people sometimes test more than once a week saliva-based PCR tests and you see we had an outbreak but detected it very quickly we're able to maintain with this one exception but again we're able to contain that very quickly rates of positive incidents less than 1% based on these population level sampling over the course of the fall term. We've also worked on other dynamic models including some work developing a COVID-19 event risk assessment and there's an Italian version that some of you may be aware of it's received multiple millions of views since we launched and happy to discuss that some other time. Okay but viruses do as you know infect organisms across the diversity of life. And also just to point out I believe there is gonna be one set of speakers who is going to talk about models of COVID-19 later in this and there'll also be a forum. So you will get a chance to learn more about the sort of class of models and infectious disease models by a few speakers later on. But viruses do infect organisms across the diversity of life not only charismatic humans, mammals, birds, et cetera but also microbes including eukaryotes as well as archaea and bacteria. And just to give you some indication that these viruses can also be somewhat charismatic as well. Here are some images at least of the virus particles. And the bulk of the work looking at virus micro-dynamics often goes through the same paradigm as Lurie and Delbrook wishes to think about viruses as agents of mortality. Here are three particular examples where I'm showing what happens when you have a culture alone e-hux, algae, and here is prochlorococcus, merius med4, ubiquitous cyanobacteria found in the open oceans at high densities globally in the surface oceans. And then here are examples of what happens when you add viruses. And you can see the decay in density and the increase in viruses in this last case actually was timing of looking at the decline of host DNA as well as the intracellular and extracellular development of phage DNA. So the takeaway here is that viruses act at these microscopic scales across a diverse set of hosts to infect and reduce the density of the host increasing their own density over time. You can learn more about this generally in this very nice popular book and this goes well beyond virus of micros by Carl Zimmer, it's called A Planet of Viruses. And you will find that it would be a nice evening read. It really spans the scale from oceans. This is not to scale pictorial of a Sahano phage right here on the surface, on the cover, it made the cover but also viruses of humans and so on. And this will not be an easy bedtime read but if you're really interested in getting inspired and wanna learn more, I've also written a book called Quantitative Viral Ecology. It's meant to be a graduate level, intro graduate level textbook but it also can be a guide, Dynamics of Viruses and their microbial host, it was published in late 2015. Okay, so what am I gonna do in these three lectures with this introductory material in mind? Today I'm gonna try to go through, as I said, principles of eco-evolutionary dynamics trying to give folks an idea of some of these core ideas of how we can think about virus micro dynamics and begin to think at multiple scales, connecting microscopic mechanisms to emergent population dynamics and hint at least a little bit at some of the ecosystem consequences. But in the interest of time, I won't get into that as much as I've done in some other contexts. In the second lecture, I will try to extend the scope beyond what I will do today which is largely a predator prey paradigm and then talk more about parasite host paradigms. And of course, we know phage are parasites but using the language and context and thinking of epidemiology may take us in some new direction. So I will do that tomorrow. And then on Thursday, I will connect some of these principles to applications and I will choose just one rather than on an ecosystem context. I will choose a biomedical health context and begin to show efforts to use phage as therapeutics and explain, in my view, why thinking about virus micro dynamics again as a dynamical system may actually aid in efforts to treat multi-drug resistant bacterial infections. So that's what I'll try to do today. Principles tomorrow, expand these principles into some new directions and on Thursday, go towards therapy. And Jacoby, you'll let me know if anything goes wrong but otherwise I'm gonna keep plunging ahead. Absolutely. I also let you know if there are questions or changes. Okay, great. That's perfect. And again, throughout, I will try to connect theory and modeling with both fundamental challenges as well as real world applications, as you can see. And obviously this will build towards this real world applications even further as we get to the focus on Thursday. Okay, so again, principles today, more on principles really on the switch between lysis and latency tomorrow and Thursday connecting theory to therapy. Good. So there is a question actually from Ayan. So Ayan, please mute yourself. Yeah, am I audible? You are, I can hear you. Yeah, so Professor Witz, I was just wondering from the Luria data group perspective. So you have a Poissonian dynamics coming in. So I was just wondering if you have a larger amount of population of these viruses, do they actually try to get in the CLT? That is like a central limit theorem and get it to like a normal distribution or so. And I'm just asking this question from a perspective of gene transcription regulation dynamics. So when you have this unregulated dynamics of some transcription factors, you have this Poissonian dynamics coming in. But whenever it's something it's getting regulated by a transcription factor, you go away from this Poissonian dynamics mostly. So is there something similar? Yeah. So thank you for the question. As you can see here, you brought up a number of different ideas. There are certainly notions in which the viral takeover of a cell can be described through the process of stochastic gene regulation just as we can think of a cell's dynamics is through that process. And if we have some unregulated gene and then notions of a Poisson like distribution of transcripts and even proteins can emerge and certainly in certain limits that can look Gaussian. But that really is beyond the scope. We don't need to invoke that to understand the fact that what we're looking here is that outcome and if resistance here has a largely to do with surface resistance, so the viruses aren't even getting in, that we don't need to ascribe all the processes that could be interesting to explore in some other contexts. Well, we could just think of it as the outcome of those cells, those colonies didn't even enable or permit the viruses to get inside. We could have a separate discussion on intercell resistance, whether resistance modification mechanism or CRISPR-Cas immunity, and that would turn out different. And we might need to think about gene regulation there. We certainly have done in other contexts. So hopefully that helps. This is strictly the colonies are resistant. We don't necessarily need to invoke the details, the intercell or details to understand that then that colony, it's offspring inherit that same feature of being resistant. And that's why we get a Poisson distribution at the level of resistant columns. Okay. Thank you. Good. Why don't I keep moving ahead? Jacob, is that good? Yeah. Great. Okay. So what I'll try to do today is explain a few things. And I will essentially give you an introduction to how viral infection can change microbial population dynamics, because, but you've already seen that we can't stop at population dynamics. We have to think about evolutionary change. So I will then go in that direction. And then we'll see how far I go. I have about 35 minutes. I'm gonna try to use it all to really give you this broad introduction and expand some of this in the direction of virus host dynamics in complex communities. Okay. So how does viral infection change microbial population dynamics? Well, to do that, and again, since I'm lucky to be here at the early start of this thing, and you've just had one introductory lecture, and I'm sure many of you have heard of Laka Volterra. And a long time ago, Vito Volterra, and it's always fun to say that name when we're here in a Trieste Italian conference was convinced by a son-in-law in Bertha, Doncona to examine fluctuations of the Adriatic fisheries. Why is it that we see these fluctuations? Is this all exogenously driven? Or can there be the result of endogenous interaction? And the first case that Volterra considered was a two-associated species. One would multiply indefinitely because it would just keep growing, but the other one would die if it was left alone. But the second one, the predator feeds on the first, the prey, and the two species can coexist together. In modern language, we would write down the model that Volterra and then Alfred Laka independently proposed as a coupled system of nonlinear differential equations where the dots are known to the derivative. Here we have the indefinite proliferation. Here we have predation, conversion of prey biomass into predator biomass, and the death of this predator if left alone. The outcome of this are these predator prey oscillations where the predator peaks tend to be shifted to the right of prey peak. So we have a prey peak, then predators rise in abundance, driving down prey. As prey are driven down, then predators decline, prey go back up again, and we see the cycle continues. We could then superimpose this on a prey predator phase plane and note that we get these cycles and they're counterclockwise. And the reason they're counterclockwise is again, we have a prey peak, which leads to the rise of predators. The rise of predators leads to the decline of prey, and the decline of prey leads to the decline of predators, allowing prey to restore, and so on. You will notice that this seems to be a closed orbit that is true, which means that if you had a different initial condition, you'd have a different closed orbit, which in physics would be terrific news. We'd have a conservative system, but that is not good news for biology because it means that the initial condition is remembered forever. These are not true limit cycles. So just keep that in mind as a caution. Of course, later models did have true limit cycles, and that was often because there was some handling time for other features of the interactions. Again, which is that prey peaks before the predators, they're lagged, and then the oscillations again, appear counterclockwise in the prey predator phase plan, as you can see here on the right. These ideas of Lacan-Volterra really sit at the heart of how the field of virus micro-dynamics has emerged, beginning in work by Bruce Levin in the late 1970s, along with Frank Stewart, mathematician, and Lynn Chao. Bruce is now here at Emory and Lynn as at University of California, San Diego. And in their view, they viewed this system, an experimental system of having a phage, a bacteria, and something for the bacteria to eat on as a resource, a prey, the bacteria, and a predator, the virus. And the idea really goes back even to Alan Campbell in the 60s, that these phages, these viruses that exclusively infect and lyse bacteria, we can think of them as a simple predator. And the reason or rationale is that they act to convert prey biomass into predator biomass, and also they never lead to the death of the prey through that process, okay? So this Lacan-Volterra model in a more simplified form, again, is the basis for these virus host population dynamic models. And here, again, you can see this simple resource prey predator model. And this is a model in which we're envisioning a chemostat in which there's a rate omega in which resources are flowed into the system and a rate omega at which everything is flowed out, including resources, prey and predators, the bacteria and the viruses, the prey take up resources, converting it into new prey, the viruses infect and lyse bacteria leading to beta, this birth size of new viruses. And what you can see is that if you start a, in silico-chemostat with a certain number of prey and resources and add a virus, you get oscillations, you get a decay, a decline, excuse me, in prey density because now it's being top down rather than bottom up controlled, and you also see these oscillations. Although it's hard to see here in this log space, we can project this onto the phase plan ignoring the resource level, and what we see are these counterclockwise dynamics, right? And the counterclockwise dynamics are for the same reason that we have these Lacan-Volterra-like dynamics, that we have a peak and viruses driving down the host density, leading to a decay in the viral density, we allow into the restoration of prey density and so on. In this particular set of equations, this should actually relax back to any equilibrium to a fixed point. So just to remind everyone so that we're on the same page, this is a bit of the life history of a bacterial virus. I'll go through this probably once in each lecture just to make sure everyone remembers it in case you showed up for one, I'll probably do it again, but also do it a little bit faster each time because I'll assume you will have remembered it. Here we have this 50 to 100 nanometer size passive bacteriophage. It's diffusing in natural environment, comes into contact with a bacterial host, injects its genetic material into the bacterial host, takes over the cell machinery as it was alluded to by Ion, and then through a time process leads to both the encapsulation of the genetic material into the capsule of the host, the self-assembly of these, excuse me, of the virus and the self-assembly of these viruses and through the release of both home and lysine genes, there can be a homemade and intermembrane, a homemade in the cell wall and out go the viruses and the life cycle continues. So this is just a process by which a parasite takes over a host, a microbial host and you can see there's a time that it'll take between when this happens and when this happens, between adsorption, encounter, infection, injection, et cetera, and lysis. And so obviously the earlier model didn't have this. There was an assumption of an immediate conversion of prey, bacterial, density, biomass into that of the virus. So obviously we need to make some corrections there and this is all done in a particular context, right? This chemistat context in which we were envisioning that media is being flowed in, there's some dynamics here, but everything is going out through waste which we can then measure and observe. So these types of models can also be extended to include models with an infected class. And the point I'm showing here, for those of you familiar with reading these is this susceptible host, infected host and viruses. The only difference is that rather than immediate lysis, now we have an infected class which decays at array 8, so in other words, one over 8 is the latent period and we get new viruses. The point is that in this model, we get a true limit cycle. Again, counterclockwise dynamics, but leading to a true limit cycle. You might not like that because you might say, well, a rate eta of decay means that we have an exponentially distributed distribution of latent periods and the peak of such a distribution is at zero and that's too soon. We could also make an explicit delayed set of differential equations in which the infected bacteria, are produced at a rate phi and V, but then this subscript tau means the number of bacteria and viruses tau before are those that are released now. These become more complicated to deal with for various reasons. As you can see, instead of having a finite number of initial conditions, here you need an infinite number of initial conditions because you have to go back in all the times between zero and negative tau. There's also this decay because some of the bacteria that were infected before, not all of them survive because some of them are being washed out through the chemistet, which is why we have this e to the minus omega tau factor. Nonetheless, in this particular model, the quantitative details may differ a little bit, but the qualitative features remain. We again get these counterclockwise dynamics. So we have this robustness of an idea from Locke-Volterra that could be applied to virus micro dynamics, which is the same notion of a simple predator-prey system should lead to endogenous oscillations of this counterclockwise type. And just to put a little mathematical checkpoint here, as I assume that you're going through in these non-linear dynamic tutorials, that it's not inevitable just because a virus can infect a host that it can invade, but rather we need to think of this as in some ways a destabilization of a otherwise stable fixed point, which we just have bacteria. And so you need to look at most simply the linearized system and check to see if the eigenvalue was positive and that would imply invasion. I go over this in the book and on Tuesday's lecture, I'll actually elaborate on intuitive criteria that can explain this as well. Okay, so just to remind folks that it's not inevitable, not every virus just because it infected bacteria, the ecological conditions have to be sufficient, which depend on life history traits as well as the abundance of the host. So just, can I finish this thought or you had a question, Jacopo? There is a question from the audience. If you want to go on, you prefer, you can wait otherwise. Let me just finish this one side, this few more slides and then I'll take the question just because I don't want to lose the train of thought here, which is these same types of dynamics can be observed in the laboratory. These are lockable ptero-like cycles between phage T4 and E coli B. You can see the population density time. So this is about a 10 day experiment where we have large scale endogenous oscillations. And you can see that the ratio of virus, those can be quite large on the order of hundreds, if not thousands. There's also a time shift here so that when the bacteria peaks, it's usually followed by the virus peak. And again, this is in a chemist stat system where it's otherwise homogeneous, shaken and not being driven by some exogenous change in resources. So just to point out here that this really is a demonstration that there can be a feedback between virus and host that lead to endogenous oscillations. That's why I just wanted to get this one idea out then I'll take the question. These original models of virus host dynamics presuppose a simple one virus one host relationship. If viruses act like predators, we should expect cyclical dynamics whether we use these simple lockable ptero-like models or ones that take into account the microscopic details of infection and lysis. And reminding folks that invasion is not inevitable, it depends on traits. And this has been observed in experimental systems. So this would be a good time to take your question. Yeah, thanks. I just had a very quick question a few slides ago when you were talking about the delays and you had this end sub-tau. Can you just, you went quickly over that. Can you just say again, what is tau and are you integrating over tau in that equation? Right, so tau is a fixed latent period. So you should think of this as N of T minus tau. So this is interpreting this would say that the change in the number of infected cells now is equal to new infections minus infections that happened tau ago that are now lysing. Good, and when you say an incident number of initial conditions, you just mean you have to keep track of tau's worth of time data to be able to run before. Correct, and so just to point out for people who are not so used to it that it's just a different way of thinking about this particular system. And oftentimes what people do, if they don't want to do with the late differential equations is to set up a finite number of stages which replicate these kinds of shapes of distributions and then you can go back to this ordinary differential equation approach. Good, and is the set of solutions to that differential equation really an incident dimensional parameter space or I mean it really different for, I guess it's different for every n-tau function. So just keep in mind, remember n tau is not a function that says n of t minus tau. So you're just getting a one set of NIV solutions but to figure out what happens now you need to go back tau ago. So just because of that delay. Revitational conditions would have n as a function of tau for that period of time. And if n of t between zero and minus tau, minus tau ago in order to integrate for. Thanks for that. Yeah, great. We're good, Jacobo? Yes. Yes. I'm plunging ahead, here I go. Part two, but I'm on pace. I'm gonna finish. So I've set things up here intentionally so we have ecological dynamics but I've already told you, Lurian Delbra told us that we should expect evolution if not co-evolutionary change. So I'll try to give some sense of this question how does co-evolutionary change and evolutionary change affect these population dynamics? So let me go back now to this experiment which I showed you in which we have these endogenous oscillations, lockable ptero like oscillations between viruses and E. coli. And what I wanna now show is something different and I'll switch back between them which is that for the first 200 hours or so it all looked like theory was fine and we'd be done but past that time something else happened. This is the same chemostat but now we see essentially a flat line of hosts and oscillations of viruses. And given the size of this crowd and the context I'll just point out that the fact that viruses are increasing implies this is a chemostat they would otherwise decay they're replicating on something but what's interesting here is that the host density remains apparently flat which doesn't seem to make sense. If you saw this time series and this time series you wouldn't necessarily relate them and this is why this is often called cryptic dynamics. What happened in fact is that they went and observed that this host population was not homogeneous anymore but in fact was comprised of two different populations one that seemed more susceptible and resistant to the virus that isolated it, marked those and then we're able to repeat the experiment in some sense by being able to track the two types independently and what they found is that what happened was that there was the emergence of resistance. So a subpopulation was resistant rose to a high abundance but there was still a susceptible subpopulation that viruses were replicating on this subpopulation and if you'll notice these dynamics look like a Volterra like between the virus and the susceptible host in terms of being phase shifted but also the susceptible host oscillations note the log scale would just be noise in the background of the resistant host density implying that we do have the emergence of resistance and there's essentially an evolution of the system in which the virus have induced evolution but not lean to their own extinction but rather than to a new kind of dynamic. So again, just to point out that these resistant hosts invade obviously they have that benefit but they don't exclude the susceptible host because they come with somewhat of a cost and if there is a trade off between growth and resistance or defense then these two different types can coexist which leads me to a more general point which is that when you have predator prey like dynamics in a virus microbe system you can get these canonical predator prey cycles locker Volterra cycles when you have evolution you can get cryptic cycles or anti-phase dynamics and that's a more general problem in the field of rapid eco-evolutionary dynamics and has been seen notably in other predator prey systems including that of rotifers and we also have a multi-type possibility as well. So this is no evolution I'm about to explain why something even funkier can occur where it seems like the prey peak is following the predator peak in other words prey eating predators not the case but something about the system has fundamentally changed when there can be co-evolutionary dynamics and just to make this more explicit here I've taken a system now of two viruses and two hosts so we have co-evolution in the sense that there's the change of the frequency of genotypes in a population over time you can see the shading here these dash lines denote the virus strains and the darker lines denote the host strains and when you add them together the total virus and total hosts seem to have a predator prey like dynamic but shifted where the virus peak precedes the host peak. Okay, so I hope that's clear. You can see also this in a phase plane where when you get one of these clockwise cycles what this implies is that rather going around this way it goes around this way which is not what we expect because it means that the peak in predators is then followed by an increase in prey and we can understand this by recognizing that at the same time the total population is changing we also have changes in the fraction and the frequencies of genotypes here host and here viruses and I've denoted them by having these high vulnerability types and these low vulnerability others defense specialists and then we also have viruses that may have low offensive types and high offensive types in terms of being able to get in more efficiently and otherwise not but they differ in their decay rates between the types and what you can see here as at the peak of the system from the perspective of predators we have a lot of high vulnerability types which leads to an opportunity for these low offense types to invade but as these low offense types invade on the viruses then the system can shift to low vulnerability and these low vulnerability hosts can do exceptionally well in the system of low offense phage. Now when there are many prey around that happen to be low vulnerability but because there are very few phage then there can be a benefit for the high vulnerability types to invade and as they do that also comes with a rapid shift to high offense types restoring then the virus population. So we have a joint dynamics of population dynamics and evolutionary dynamics and it's really driven by the concurrent change in genotype frequencies. Does this happen? Well, in work by way at all working with Bruce Levin they had observed what they viewed as complex dynamics of Vibrio cholera and its phage and cholera and phage have its own interesting story which you can see here are dynamics that look as I said complicated but we notice something interesting here when we focused on a few sections and I've highlighted them and raised them in the line with here so that you can see them and I will then project these on the next slide into the phase plane and what we found were there multiple examples of clockwise cycles. And there was actually further evidence that the system didn't just have a single host or virus but in fact they had found this T and B phage making turbid or big plaques and multiple kinds of resistant hosts and what you can see here is that we have these clockwise like dynamics where a system not only goes around the wrong orientation but gets back nearly to where it started. Of course, one can raise a question is this sufficient evidence for a clockwise cycle? And so what we did was in some sense take that time series and then create random time series that had the same point to point correlations reconstruct synthetic time series and ask how often would we see these kinds of short clockwise like cycles and then see if the fact that we found these should be a surprise and the answer is yes, it was surprising despite the shortness of these cycles. The idealized clockwise cycle has a winding angle of two pi and goes back exactly where it starts. Here's the distribution of all these synthetic time series what we observe in red and just to point out that this is essentially as good as the link's hair evidence as well which is the canonical example for counterclockwise cycles or prior prey dynamics. So we have as much evidence as we have essentially for these phage vectors we did for the link's hair. And so we have examples now of clockwise dynamics in this co-evolutionary system. So just to sum up the second part that more generally whether we're talking about phage micro dynamics or prior prey dynamics with evolution in general sense without evolution we can only have these counterclockwise cycles in a qualitative sense. When either evolved but not both we can have this or we can have anti-phase cycles of the kind that you could see or even these cryptic cycles where one is changing and the other is not. And when co-evolution is included then either of these two things can happen but also it's possible to have clockwise cycles. So the take home here is simply that a rapid change in genotypes can impact ecology. So when we think about virus micro dynamics we can't think as evolution has just turned off. And again, this is a natural consequence of going beyond Luria and Delbrook and asking what happened next like Luria did in the 1940s but not just on a plate that's static but actually thinking of it as an intrinsic part of the dynamical system. But in this last part in the last 15 minutes I'm gonna ask what other dynamics emerge in even more complex communities. And I should pause here again in case there are questions. Yes, there are two questions. So Miguel, please mute yourself. Hi, hello Joshua. I have a question for the clockwise dynamics. Are we assuming in the system that the aggressiveness or the vulnerability have a fitness disadvantage or advantage beyond the viral micro dynamics or why else will the low aggressiveness genotype for example catch up again? Right, so we are assuming that there are trade-offs in traits. So what I just said before, it's not inevitable just because you have co-evolution doesn't mean you have to have clockwise cycles, right? There could be a replacement and we could just knock out one of the other kinds maybe the emergence of a doubly resistant bacteria and even the fact that there's some trade-off in growth it still knocks out the first kind. But there are particular conditions which we go into in this paper in which these cycles can generically be seen. But you're right that it involves trade differences which I'll elaborate on next. Cool, thank you. And there was another question by Ayan. Maybe we can just because we've, I've heard from Ayan once and I appreciate that but just to make sure that given there are hundreds of people here maybe I'll just keep going to part three and Ayan you can send me or something in the chat just to make sure we hear from multiple folks. Is that okay, Jacopo? Yes, okay for me. So Ayan why don't you just send me a, put it in the chat and I'll answer after or just to make sure that I finish up part three. Sound good? Sure, sure, sure. Thank you so much, very good. Okay, so let me go to part three and ask this last question which what is the relationship between infection networks and host viral dynamics and complex communities? As you can see I've structured this talk focusing on single virus host dynamics then two in one and two in two and this would be a very long talk but I only have 10 or so minutes left. So we're going to try to make a leap of a kind and this leap has been possible with really almost a decade of work by Cesar Flores who began some of these projects continued by Luis Jover and continued even further by Ashley Kunin in the group now and all these are physics students doing this kind of quantitative bioscience stuff. And again, I'll go back to this notion that there are many viruses in these systems and pointing out that when you have this many viruses they're going to be quite diverse. We went back to some of these original data sets to really hone in on this question as part of a collaborative effort to analyze a virus micro dynamics in natural systems finding that if we look at the number of pro-carats, larger bacteria and viruses per milliliter, you can see relationships. You may have heard of this notion that there's 10 to one viruses per bacteria in natural systems. That's not necessarily the case. So that's a decent median. There's natural variability between one to a hundred to one. There's more of both in the surface than there are depth. But the point I'm trying to say here is that there's a significant amount of variability and there's also just a significant number of viruses that tends to be many more viruses than there are bacteria in a typical ocean community, which means there's a lot of different types. And this has often been very hard to estimate because of the problem of rarity. So there's some early work 15 years old now which estimated the diversity in terms of species richness between 10,000 and 1 million viral genotypes. That's a lot also says that estimating is hard and that estimating problem remains hard. There's something fundamentally hard about understanding the abundance of rare things because you don't see how many rare things there are because they're rare. So just a side note, but sufficient to say that these really are complex, abundant men diverse communities. So how do we actually figure out who infects whom? We can't just keep going with these simple models. We actually have to look into natural systems. And so that's what we began to do to get a sense of what some of these relationships might look like and how that might explain coexistence. So what folks in the field have usually done is like Lauren Delbrou collect bacteria and phage from the environment or from experiments or evolution experiments and then see who infected whom. As you can see here, we have a plate of bacteria and you can see as different kinds of bacteria exposed to different viruses. Sometimes these viruses make these clear holes. These are plaques, which denote clearing. And then here they added the phage but there was no clearing to note that this particular bacteria was resistant to this particular phage. People repeated this many times over characterizing these as susceptible or resistant. And here you have one example of a paper in our digital version just to point out that these are the same thing where the blue background denotes the fact that the phage in the column can infect the host in the rows and the white scares denote the fact that they can. When we looked at many such patterns across many different systems, we weren't sure what to expect. And if you look at this, you can't really see much of anything and first we were disappointed. We realized, of course, there are many ways to display these particular results of phage bacteria infection experiments because you have row and column orders and this becomes a large, exponentially large number of combinations. So we used heuristics used to analyze network systems more generally to look for latent structure. And in fact, that's what we found. Examples in which it seemed like nestedness was quite typical. And what I mean by nested is that we have these, remember that viruses are in the columns and host in the rows. You can, let me see if I have an example. Yes, good. Here's the original data here and here's the restructuring. This is exactly the same data. I just wanna emphasize. Same data, we've just shifted the rows and columns revealing that this is in fact more of a nested structure where we have these specialist viruses which tend to infect a few hosts. It's not perfectly nested, but it tends to be so. And they infect the host that everyone else can infect. So the specialists seem to be infecting the easiest to infect of the host. And likewise, the general seem to infect the hardest host to infect, right? So the virus general is are infecting both the easiest as well as the hardest. And you see that then the infection ranges are nested one within the other and the same with the host, right? So even though this wasn't apparent in the original studies it was clear that nested in this seemed to be quite typical which raises questions, right? And the question that raises is how do we have coexistence potentially between these specialists which seem to infect the host that everyone else can infect and the generalists, right? And likewise, why do we have hosts that seem to be infected by everyone hanging out with hosts that seem to be infected by almost none or very few. And just again to point out this was unexpected the nestedness in the original displays were quite low compared to the ones that we found with this revised sorting. And again, this means that we have these phage bacteria networks that are typically nested and it's common in both ecology and evolutionary studies. So how can they coexist? So let me give a particular example here of one which why doesn't this most resistant host outcompete the rest, right? It's only susceptible to one virus but so is everyone else and it's not susceptible to the others. And likewise, why isn't this most specialist virus outcompeted by the others? Same reasons, only in fact one thing, so can everyone else. What we've done is take these dynamical systems that I've already explained but then using this letter I and J to note the fact that we have many types so the hosts are competing they're being infected and laced by viruses which are then releasing new virus particles back into the environment. And I'm only gonna point out the fact we have this matrix M which we now are going to use something based on what the measurements imply rather than early kill the winter models which say there's one virus for every host and clearly that could lead to coexistence. We're going to replace that with these nested models raising the question of how do we have coexistence when we have overlapping niche or overlapping host ranges? And what we can see is that if we take a very simple community when we have two viruses and bacteria together in one case, only one coexist you can see host one survives excuse me, yes, host one survives and here we have virus two persisting and virus one going away this other host may be at low density and here we have both of them coexisting together and they both have a nested network but now the strange differ in their life history traits. So one case one gets excluded but in the other all of them coexist and they have the same structure but it's the life history traits again that make the difference. If we solve for the steady states in the model I'm just gonna point out you see these kind of differences of traits R2 minus R1, the differences in the infection efficiency so it seems like these steady states depend on differences in terms of growth rates and differences in terms of viral life history traits and the key points without going into all the details we've elaborated this for quite some time is that if there is a growth rate that decreases with defense so in other words, most vulnerable grows quickly least vulnerable grows slowly and likewise that the efficiency of the specialist is high in other words it draws down host to low densities whereas the efficiency of these generals is not as high it doesn't draw down the host to low densities you can get arbitrary levels of coexistence so viruses and hosts can coexist with arbitrary complexity. Now this does raise the question is there evidence for such trade-offs? And just to point out that typically when one looks for trade-offs you see a tendency for there to be a growth rate resistance trade-off and a fitness and host range trade-off for viruses but I'll also point out here's strain and growth rate all of these seem to be resistant to this particular virus that there are examples in which there doesn't seem to be any cost and likewise here, fitness on original hosts no cost even though now it has this niche expansion there are other interesting stories here about contextual benefits of fitness able to infect some but not other hosts but again points out that these relationships are statistical in nature just like those of the of the nestiness in these communities. And so on a separate work we looked at the relationship between biodiversity in other words richness of this community as a function of nestiness and only to find that nestiness does seem to promote diversity in the system even if the nestiness is imperfect and this depends on the life history traits and we've done this for various kinds of life history trade assumptions and trade-offs but again the tendency remains. So just to finish up here I'll just make one last thought and then I'll conclude which is I've made a point here from single to multiple to these complex communities showing that there is mechanisms of coexistence whether through revolutionary dynamics or through trade-offs but as nestiness the only feature and I don't have time to fully elaborate but I'll just give you a caution that most of the studies looking at host range and infection dynamics focus narrowly on a particular phage and bacteria within a species or genera but clearly if I have a phage of E. coli it's unlikely to also able to infect prochlorococcus and synococcus I can get it to you won't happen. So we clearly have differences at other scales and just to point out that a long time ago and we continue to work on related problems we found that in these large scale studies of ocean systems here was the original data which we then restructured and identified modularity and found large scale systems did have modularity where the bulk of interactions happened within these modules. And so this just again suggests that it's not only nestiness that there is separation, some phage are affecting some types. What we found is these modules were correlated with geographic diversity. This is from an open ocean Atlantic sampling system and even within modules there tended to be nestiness. So in reality, what we expect is that true network structures multi-scale and that remains a challenge for the field as a whole. Okay, so I think I'm just on time and wrapping up just to point out that trade-offs facilitate coexistence in this last part that the abundance depends not just on who they can infect but on like history traits that these trade-offs need not be perfect for coexistence. Obviously we saw that in terms of the nestiness it was not perfect nestiness nor was the trade-off necessarily perfect but just as a caution large scale networks may have different structures and I anticipate I'd run out of time but we continue to work on actually the joint analysis of genotypes and phenotypes and if you wanna see some of that work this is with Justin Meyer it just came out on BioArchive going beyond just these phenotype assays and linking them to genotypes as well. And with that I wanna thank you for your time. I went over a lot of material but my hope is that for many of you who are new to this area this gives you a broad overview of some of the challenges as we move from microscopic dynamics to build population models, evolutionary models and begin in the direction trying to understand virus micro-dynamics and ecosystems. Thank you and I think it's probably time nearly for a break. Yes, so thanks a lot Joshua that was a fantastic broad introduction. So there are actually two questions so if we can, I think we can take five minutes for question, okay. So there is one question from Leonardo. Yes, thank you, thank you for the lecture professor. I wanted to ask and I'm sorry if I'm asking something trivial but I wanted to ask if there are explanations or intuitions as to why the relationship between phages and hosts is nested. Right, so that's a terrific question and one that has bugged me for quite a long time because it seems to imply a kind of arms race dynamic is it a question of evolutionary constraint or is it something about the ecology? And I won't open up my slide deck to be tempted to kind of give you yet another lecture on the questions but if you look in our paper by Gupta et al we begin to ask this finding that in some cases it seems like it's really the ecology that's driving it not necessarily a fundamental constraint from the evolution of from the let's say the biophysical side. It implies that there's an ability for a phage to then have this host range without necessarily this earlier cost, right? And likewise for there to be the possibility of becoming resistant to prior phage and yet still then being infected by a new phage type. So in a co-evolutionary sense it implies an arms race like dynamics which would give rise to nest in this but yet in this paper Gupta et al we show that even though that's what the phenotype looks like the gene type implies that something else might have happened but there was some trade-off or constraint ecologically that didn't permit a fluctuating dynamic in which case you might expect modularity rather than nest in this. It's an open question, a terrific question. So I'll just leave it there that it's one that we continue to try to explore really gets the heart of what we're trying to figure out. Okay, thank you very much. There is another question from Martina. Yeah, thanks Joshua. It was really interesting and my question is more a curiousity I would say because from what you told us it seems that there are if there are very few generalist viruses and a lot of specialist viruses and I see a sort of parallelism with the distribution of generalists and specialist in bacteria because again in natural systems there are very few generalist bacteria and a lot of specialist bacteria and I want to know if you have a comment on that or if you can comment on this. So I guess I'll comment from the theoretical side that I didn't explain necessarily the relationship between the host range and the abundance but you can actually go do that and it turns out the model is flexible so I know that may be unsatisfying but it could be in the model predictions that the generalists are more abundant or even less abundant than the specialist and it depends in some sense on their difference with respect to the most similar host or virus. I'd also caution that the generalism here is still narrow from the virus side because we're talking about generalism within the context of probably a species or perhaps general not somehow beyond that so just to caution but you're right that it really depends on the life history traits and the trade-offs but at least in the model it doesn't say that absolutely one or the other will be the more abundant kind but again the caution here you're probably thinking about metabolic generalism and so on and here it's just still narrow so we don't yet have a sense I don't think enough quantitative data to give a definitive answer on the virus side it's something we're still working on. Great, thanks a lot. There is one last question by Mike and then we'll take a break. Yes, hi Joshua, thank you for the talk. I was hoping if I could give your opinion on particularly this connection between virus host dynamics and scaling up to ecosystem level consequences. The example that I had in mind was the unfortunate fact that we are currently destroying biodiversity at unparalleled rates and how might the viral respond to this? Obviously coronavirus is one example of this but I just wanted to hear kind of your professional opinion on this how we could understand equal evolutionary consequences of this. Yeah, so that is probably not a question I can answer even in one minute to the extent to which we're thinking about that question just because it's such an important broad question. We have begun work which I'd hoped it would almost be right at this point but it's still maybe a few weeks away but hopefully we'll be out soon on the bio archive to embed these virus micro dynamics in the context of ecosystem models in which viruses are not the only agent of mortality but it also includes flagellates and other protists that might be grazing upon target hosts. And so we really need to think about viruses as part of these complex communities. And once we start changing things and particularly one of the things we could change are things like salinity, right? As well as CO2 levels or even temperature that's going to change virus micro dynamics in ways that frankly concerns me but I don't know the extent to which that will start to impact long-term let's call them microbial loop mediated processes but I think we should be concerned that in addition to tampering or somehow upsetting biodiversity we're also messing with ecosystem function. I'll point out that we do have one little spec of the paper on micromonus viruses and hosts and affects putatively of temperature and long-term scenarios where it implies that at least current viruses may have a hard time keeping up or infecting with certain bacteria and to the extent to which they play a role in shifting the fate of dissolved organic material that may also mean that it's really beginning to transform and change carbon and nutrient cycles at global scales. But at this point that's all I can say that we're at the beginning of that process but that's one of the reasons we're focusing so much on these ocean systems because of that shared concern. Thank you. Great, great, thanks a lot, Joshua. So Joshua will give a lecture again tomorrow and what we're gonna do now is to take seven minutes break. So...