Scientist Stories: Andreas Mayer, Quantitative Models of the Adaptive Immune System

All right, I think it's time to get started. So let me say hello and thank you to everyone around the world for joining us for this week's lab meeting. My name is Kristin Aboud. I am the science editor at the Human Vaccines Project, and I will be your moderator today. The full extent of COVID-19's devastating impact is just now becoming clear. An effort by the World Health Organization to more accurately calculate how many deaths can be attributed to COVID-19 shows that around 15 million lives were lost globally by the end of 2021. This is drastically higher than the previous estimate of 6 million, which was based on combining numbers officially reported by individual countries. The WHO's latest calculations rely on national data combined with new information from localities and household surveys, as well as the use of statistical models that try to capture previously unreported deaths, including those that occurred as an indirect effect of the pandemic. More than a third of the additional 9 million deaths this new report attributes to COVID-19 are said to have occurred in India. Before we get started with today's presentation, I wanted to announce that the application link for the 2022 Michelson Prizes is now open. These next-generation grants are awarded annually, annually, excuse me, to support promising early career investigators who are working to advance human immunology, vaccine discovery, or immunotherapy research. The Michelson Medical Research Foundation, together with the Human Vaccines Project, established these $150,000 prizes in 2017. More information on the prizes, as well as a link to the application portal, are available on this slide, as well as on the Human Vaccines Project website. So please check there for more information or to apply. Just one more note before I introduce— oh, pardon me. Just one more note before I introduce today's speaker. The information presented today includes some pre-published data that is currently under peer review. We therefore ask that you not reproduce or disseminate the data presented in any way. Now it is my pleasure to introduce today's speaker, Dr. Andreas Mayer. After initial training in statistical physics in Göttingen and Paris, Andreas obtained his PhD at INS Paris for his work studying how evolution shapes immune defense strategies. As an independent postdoctoral fellow at Princeton University's Lewis-Sigler Institute for Integrative Genomics, he broadened his research to study the question of how T-cell dynamics are regulated. To address this question, he has developed theoretical and computational approaches to make quantitative sense of the recent deluge of sequencing data. As of this month, Andreas has set up a quantitative immunology group at University College London, and he is excited to do so at a time that is ripe for major advances in the grand challenge of understanding immunity quantitatively. During today's presentation, please send any questions using the Q&A function in Zoom. Feel free to use the chat for general comments, but please don't post questions there. I will ask Andreas a broad selection of your questions after the presentation, and we will have about 20 minutes for discussion. With that, it is my pleasure to introduce Dr. Andreas Mayer.

Thank you so much for that kind introduction, and let me share my screen. So as was just said in the introduction, I very recently moved to University College London to open up a quantitative immunology group. But most of what I'll be presenting today is work that I have conducted while being an independent Louis Sickler Theory Fellow at Princeton University together with an amazing team of students and collaborators that I want to acknowledge. And so I'm very excited today to have this opportunity to speak as part of the Global COVID Lab Meeting. As someone that comes from sort of a different, sort of more computational and quantitative background. And so I want to start very briefly by saying that, well, immune defence is the set of mechanisms that have evolved to protect us from disease in a sort of long co-evolutionary arms race that has been going on for billions of years between organisms and the pathogens that can infect themselves. And I have been, over my scientific career, been broadly interested in how these immune defense mechanisms have been structured by this coevolutionary process. And specifically, if you're thinking about us right now, we are most interested in how we defend ourselves against viruses, and specifically during the current pandemic, SARS-CoV-2. And so given that immune defense is one of our most potent weapons against infection, very clearly immunology has played a huge role in our current pandemic and has led to one of the major successes, I think, in our response to the pandemic, which has been the worldwide sort of rollout of effective vaccines, but the pandemic has also highlighted some knowledge gaps that relate to our quantitative understanding of immune dynamics in humans. For example, the question of why disease severity varies so dramatically from one individual to another has only been answered in part so far. And also the answer of how durable is immune memory and what that durability might depend on is still incompletely understood. And so today in my talk, I want to make an argument that for filling these gaps, we really should think about how we can build on the vast amounts of data that have been generated during the pandemic using the recent advances in omics technologies that allow us to measure immune dynamics at scale to go towards a future where we have quantitative models of immune dynamics and to really try and answer the question of how our history of infections together with our genetic background and aging shapes the collective dynamics of all the immune cells within our bodies and thus our immune state and our ability to respond to infections. And I think there's a big hope that mathematical modelling and machine learning together with this new data can really help us usher in a new area where we are much better at predicting the dynamics of human immunity and help in a way that will help us design better treatments and vaccines. And so what I want to do today is I want to illustrate why I think there's some hope that these quantitative models, despite the obvious complexity of our immune defenses, can actually help us make progress. And in order to do so, I want to share with you some research highlights from my own work to sort of give some sort of impressionistic picture of some of the kind of approaches that I think can be useful in deciphering immune dynamics quantitatively. First, I'll talk about how T cell expansion is regulated during an acute response. Then I'll talk about some of our ongoing efforts for using T cell receptor maps that have been generated in response to our current pandemic to learn the rules of how epitopes actually map onto the T cell receptors, so to crack the immune receptor code. And lastly, to maybe illustrate how modeling can be useful to think about, to help us think about the timescales over which immune memory might be durable, I will talk a bit about some work we did a couple of years ago that shines some light about how stable the T cell memory hierarchy is over dehumanization. So let me start with the first part, which is how are T cell responses regulated during an acute response. So here we started from a very simple question, which is that there's different initial frequencies of cells, and despite that, the immune system immune system somehow needs to be able to come up with a regulated response. And how does it do so? Well, we looked at a set of experiments that have been done about a decade ago in the late Bill Paul's lab that has addressed that question quantitatively in a mouse model. And what that mouse model allowed this team to do is to actually have experimental control over the initial conditions of this dynamical process, meaning that they could transfer different numbers of transgenic T cells initially and then give the cognate antigen and count the number of such cells they get after a certain number of days of expansion. And what they found was very interesting to us as theorists thinking about this system, and that's what's plotted on the right here. So on the x-axis, there is the initial number of T cells, and on the y-axis, the fold expansion, so the number of T cells at the peak of the expansion divided by the initial number. And what they found was this simple, strikingly simple relationship where the fold expansion depended as a power law with a slope of roughly minus 1/2 on the initial number of T cells. And that was interesting to us because it didn't fit with two very simple pictures of how one might think about how T cell dynamics. One being that there's no regulation at all. All T cells just proliferate independently of each other. Then one wouldn't expect any dependence here. And the other scenario being that one just reaches sort of a ceiling of a constant final number, but that would lead to a steeper dependence in this of the full expansion on this initial number. And so what does this suggest? Then to us was that there needs to be some collective mechanism that regulates these T cell responses. And in order to figure out what this mechanism might be, we went sort of to the drawing board and we asked, what's the simplest model that captures the basic phenomenology of how T cell expansion might be regulated, and can we make sense of how such a simple regulatory mechanism might explain this data? And what we propose is a parsimonious theory of regulation by antigen dynamics that only involves minimal ingredients, which is depicted here, both in terms of these dynamical equations and in terms of this graph here. So what we're saying is that T cells proliferate when they get— the signal from stimulation by the presentation of antigen-presenting cells of their cognate antigen, and they will stop proliferating when they no longer get that signal. And they can no longer get that signal either because the antigen has sort of decayed away over time, or because they start competing. And we will see that both of these scenarios can happen under different conditions. And so if we're in a scenario where competition becomes limiting, what we were able to show is that this very simple theory actually predicts a fold expansion that does depend on initial numbers as a power law with an exponent that depends on these parameters. And so without any fine-tuning, we get this functional dependence. And with biological realistic sets of parameters, we can actually explain this data of how fold expansion depends on initial number Moreover, we can also explain the time course data that shows that at higher numbers, what happens is that there's sort of an earlier peak than at lower initial cell numbers. So that's good. We have a very simple model that can explain a number of data points. But I think what illustrates best the power of simple mathematical models is what we did next. What we did what we did next was to say, well, if you look at these equations, there's a second regime, which is when affinity becomes limiting. And what would we predict in that regime? Well, if affinity becomes limiting before competition sets in, so we have a lower affinity antigen, then what we predict is that then now the fold expansion no longer depends on the initial number of T cells, but instead it depends on the parameter k, which captures the sort of avidity of the interaction between the TCR and the peptide MHC. And we were lucky that when looking for the literature, we actually found an experiment that had been done that was basically measuring fold expansion and its dependence on this on affinity. And so this is an experiment that was published again about a decade ago that has a very similar flavor, but here what has been done is that the ligands had been changed slightly by introducing single amino acid substitutions, and the single amino acid substitutions in the peptide led to different peptide concentrations that were needed to stimulate a half-maximal interferon gamma response, which is sort of a proxy for this avidity parameter k in our theory. And so we could do something very simple. We could ask, if we take these independently measured affinity values and we look at the fold expansion that they measured over the time course of their experiment, do we find this predicted relationship? And And to somewhat to our surprise, this worked out very beautifully, which is shown here on the left. So this is just taking this published data, replotting it in a way that is suggested by our theory. And indeed, we found that the fold expansion at the peak of the expansion depends as an inverse power law on the relative PMHC concentration that is needed to stimulate half-maximal response. And moreover, without any free independent fitting parameters, it also predicts the different time courses of the number of T cells as a function of time for these different ligands with different affinities. And so what this illustrates, I think, is that there is some hope that despite the complexity of our adaptive immune system, simple models can actually be predictive and can help us refine then our experimental understanding of the system and of the regulatory mechanisms that might be at play. So now, how can we go from there to the full complexity of natural responses as we might want to study them in response to an infection such as with SARS-CoV-2? Well, natural responses clearly depict The picture is more complicated. First, these responses will be polyclonal, so they will involve different sets of T cells with different receptors that target the same epitope, but then also different receptors that will target the multiple epitopes that can be presented from a single antigen or from, moreover, from the different antigens from a single infection, from a single virus.. And the starting cell numbers in natural responses are not simply experimentally controlled as in these experiments. Well, they will depend on the history of prior exposures and the statistics of the recombination machinery that gives rise to these hypervariable receptors of the T cells. And so I think there's hope that we will eventually be able to take these models to this more more complex setting, but as a starting point, what we figured we needed to understand better is the question of how epitopes map onto T cell receptors. And so we know that this is a complex sort of interaction that happens between the sort of 3D structures of the T cell receptors and the peptide-MHC complex, that in particular involves the hypervariable loops of the T cell receptor, which are sort of in most close physical proximity with the binding interface. And the question is, can we learn some of the rules that govern this interface to use sort of the abundant sequencing information that we now have available about different T cell receptors to get at this more functional question of, what are the kind of receptors that will actually target the same peptide-MHC complex. And the reason that this is a somewhat daunting challenge is the sheer diversity of both the targets and the receptors. So, on the one hand, on the level of the different targets, you can see that if you have 9-meres of 20 different amino acids, that that is going to give you something of the order of 10 to the 11 different 9-mers. You take 11-mers, you get something of the order of 10 to the 14. So you get very large numbers of different ligands that the adaptive immune system might need to interact with and distinguish. On the other hand, in order to actually specifically respond to all these different ligands, as we know, the adaptive immune system uses the amazing machinery of editorial combination to generate a vast array of potential receptors. And that theoretical diversity of all the different potential receptors that can be made by this process is astronomically large at 10^61. But even within an individual, there are sort of on the order of 10^9 distinct clones per individual. So clearly what this suggested to us is that we need to take a statistical approach And we need to have a lot of data in order to see to what extent there are rules that generalize from knowing a set of receptors that recognize one peptide-MHC to a set of receptors that recognize a different peptide-MHC complex. But luckily, and I think this is something that is true more generally for the field, there has been an explosion in data because of all the attention that has been focused at SARS-CoV-2. And so there have been a number of major studies reporting large-scale immune receptor epitope maps for SARS-CoV-2, some of which I've listed down here. So this data made us ask, what are the kind of statistical tools that we should develop in order to really use this data to inform the question of what are the different T cell receptors that might bind the same target. And so to sort of quickly illustrate the nature of these immune receptor epitope maps, the experimental strategy is quite simple. So you take a blood sample, you select from that blood sample the T cells that bind a certain target, for example using tetramers, and then you sequence the hypervariable T cell receptor chains, either in sometimes in a paired way where you get both the alpha and the beta receptor or just just the single chains. And so then the task for us coming at it from sort of a computational or a theory perspective is to answer the question, well, if we have a blood sample where we have a certain set of receptors and we then bring it through this sort of funnel of selecting all the receptors that bind a certain target, and then we get all the receptor sequences from the TCRs that are specific, how do we actually detect the selection or the imprint of selection in these receptor sequence report graphs? And moreover, beyond detecting quantitatively how much selection there has been, we would then want to answer questions such as, if a certain receptor we know is specific, what are the kind of sequence changes that we can make that will maintain specificity, and which are the ones that are no longer going to bind to that same target? And so in ongoing work, we have started to address both of these questions, and I want to quickly illustrate where we headed with that. So first, there's the question of how to detect selection, and here we've taken inspiration in population genetics where one of the basic ways that selection is detected is something called this dN/dS ratio, which is basically comparing the rate of non-synonymous to synonymous substitutions over the course of evolution. And the basic insight behind this ratio is that functional selection on proteins happens on the amino acid level. And because of the degeneracy of the codon code, synonymous substitutions should be neutral with respect to this selection. And so the question is, for us now, how do we use this basic insight that selection happens on an amino acid level in the current context of the selection of these T cell receptors? And the difference being that here the selection is acting on standing variation.. So in the T cell context, there's no mutations, there's no hypermutations such as they happen for B cells, but instead there's a standing variation that is created by the recombination process in the thymus that is then selected upon when we do the experiment and we fish out all the receptors that are specific to a certain target.. And so what we propose as a statistical measure is to use coincidence counting. So to ask, what is the probability that if we pick two nucleotide sequences at random, that they're actually going to map to the same amino acid sequence? And that comparing these coincidence probabilities is going to give us a measure of selection. And so let me illustrate why this is true. So if Here we have this graph representation of a putative sample from a T cell receptor repertoire, where each dot here is a nucleotide sequence. And these vertices are connected by edges if they map to an identical amino acid sequence. Then we can think of that the probability of coincidence is 2 times the number of edges divided by the potential number of edges, which is the number of vertices times the number of vertices minus 1. And so you can ask, how does that measure behave under different kinds of sampling? So one is just subsampling. So clearly, if we sample from the blood, we're not going to get all the receptors. We could just say, what happens if we select a random subset of cells. So you select a random subset of nucleotide sequences, and you can convince yourself that doing so actually doesn't change the coincidence probability. So then that's good. So just the fact that we've taken a sample of a smaller size doesn't change this measure. So what about functional selection for actually being specific to the same target? Well, if your specific If you're selecting sequences that are specific to the same target, that means that whenever you've selected a certain nucleotide sequence, you should also select all the other nucleotide sequences that have the same amino acid sequence because they should also be specific. And so if instead we select random amino acid sequences, you're basically selecting now not individual nodes, but we're selecting clusters. And as you can sort of see here visually, you'll get a lot more edges that remain after subsampling than if you do a sort of random subsampling of notes. And so we can use this coincidence probability as a measure of selection. And interestingly, you can actually get relatively reliable estimates of these coincidence probabilities from relatively small samples. And so we can apply this to real data And we apply this to a bunch of different datasets to look at whether there is any commonality to the way that antigen-specific selection drives the level of convergence onto a set of common solutions. And in order to do so in a bit more general sense, we looked at— we generalized our coincidence measure to not just look at precisely coincident amino acid sequences, but instead we looked at the distribution of sequence distances between pairs of sequences where we allow also for a certain number of amino acid substitutions between the sequences, which is this parameter delta here. And what we found was that across different datasets, we found a remarkably reproducible pattern where the distribution of these coincidence frequencies normalized by the background frequencies that you would expect just from a VD cherry combination showed a striking enrichment at small distances, implying that there's a very strong selection pressure on both of the hypervariable chains, together with an exponential decay by roughly factors of 10 per every amino acid that we change within the hypervariable chains. And so the interpretation of that, one can convince oneself mathematically, is that most single amino acid substitutions actually change specificity despite what one might have thought. But at the same time, there has been a lot of successful applications of clustering methods in using sequence information to find groups of cells that target the same antigen. And so why do those work if most amino acid substitutions actually change specificity? Well, this is because the probability that a sequence neighbor is binding is still orders of magnitude higher than a random receptor that is binding. And so this quantitatively this analysis quantitatively resolves this apparent paradox where on the one hand, if you do mutagenesis, you'll find that most of your neighboring sequence neighbors in receptor space will not bind. But on the other hand, on a sort of global level, clustering can be very helpful. And so what next? So beyond this purely statistical approach, you can then try and use machine learning to try and predict which ones of the neighboring sequences might have a higher probability of still binding and to learn sort of a more fine-grained distance metric. And we've framed this machine learning problem in terms of learning the model parameters that maximize the composite likelihood of the observed specific sequence pairs relative to a background. And what we found is that there are relatively intuitive physical chemical rules that are predictive of binding specificity regardless of context. For example, that if you substitute an amino acid to a different amino acid that has similar physical chemical characteristics, you're much more likely to maintain specificity. And similarly, there are certain positions along the hypervariable CDR3 chain that matter more or less for specific binding. And so what we hope to do with this is to ultimately apply these statistical tools together with the knowledge of the recombination statistics to map the landscape of precursor frequencies. So you could potentially in the future take this and ask, for example, in the vaccine, are you going to target a certain peptide where you know that a large proportion of the population will actually have— generate T cell receptors that will be public on a functional level in the sense that they have similar receptor sequences, maybe not precisely the same receptor sequences, but similar enough that it can actually target the same peptide in a similar manner. And so with that, I want to get to the third part to my talk, which is about thinking about the development and aging of a T cell repertoire that will have some— will give us some idea about what other kind of timescales we should expect over which T cell memory is actually maintained. And so here The data that we started from was cohort repertoire sequencing data in healthy subjects of different ages. And the basic question that we had was, what can we learn about underlying dynamics from the pseudo-temporal data where we get snapshots in different individuals along different stages of their lifespan? And where we started from was the striking finding that there's a very broad distribution of the clone sizes that hold across the human lifespan, where there's a few clones that are very large that make up on the order of a couple of percent of all the sequencing reads that one gets in a typical experiment. While on the other hand, the majority of clones is actually only seen once. And we came up with a simple model that could explain both how that broad hierarchy initially gets set up during the development of the T cell repertoire due to homeostatic expansions that happen as the developed— as the repertoire first forms in infancy, and how that hierarchy of these different memory T cell clone sizes is then later reordered by fluctuating selection that involves exposures to different antigens throughout the lifetime. And, well, this is a general theory that can produce these sort of power law clone sizes, but the question is what are the time scales over which this reordering happens relative to this initial distribution that gets generated during development. And so to answer that question of how dynamic the hierarchy is of T cell memory clone sizes, We tested the prediction that the early founded clones should be more likely to be in the upper tail of the cloneness distribution because of this early expansionary period. And luckily, due to a quirk in the biology of T cells or T cell development, sequence information alone actually gives us a marker about which T cells were likely to be part of the early pension, because it turns out that the enzyme TDT that is responsible for the insertions in the process of VDJ recombination is not expressed or more lowly expressed during early fetal development, such that having zero insertions in a receptor sequence or being close to germline is a statistical marker for being a clone that was founded early. And so we could look at in this large cohort, we could look at the fraction of clones at different abundances, so from the largest clones to the smallest clones that have this marker. And we found that indeed there was a striking enrichment of these early founder clones among the largest clones in infants or in kids. And what was then very surprising is when we looked over decades of human aging was that this imprint left by early dynamics was actually very long-lasting and lasted over decades in a way that is depicted here. And in a way that is described through this— the stability of this hierarchy over a decade timescale, we were able to show, can be quantitatively described by our model that sort of allows us to collapse all of this data through a simple single theory predicted curve using only two fitting parameters, one of them being a time scale over which the glonsize hierarchy varies, which we found to be on the order of a decade. And very interestingly, we found the same very long time scale looking at a very different quantity, looking at sort of more short-term longitudinal sampling within an individual. And asking how much do clone sizes of these large memory clones vary over this short period of time within an individual, we again found a timescale that with an error bar is actually compatible with this timescale that we found for the maintenance of these imprinted clones. And so together this suggests— I want to add on sort of a positive note— that at least as far as this analysis is concerned, some of our T cell memory is actually remarkably long-lived. And it will be interesting to see to what extent this is general for different kinds of T cell memory or to what extent there's variability in these timescales across different exposures. And so with that, I want to conclude and maybe leave out this slide for the discussion. And maybe as a last question, for developing this research vision for quantitative immunology, there's, I think, the question of how we as a field can further collaborations towards this goal between both experimental groups and computational groups to really deliver on this vision of predicting better the dynamics of the human immune system.

Thank you very much. Thank you, Andreas, so much. That's really fascinating work, and I love this last slide because that was going to be one of my questions for you. And obviously you've referenced how much data has been produced as a result of the COVID-19 pandemic, and I guess what do we need in terms of collaborations to actually utilize that data, and how do we get from analyzing that data to to where we actually have a predictive model? What needs to happen in that to make that more of a predictive model?

Yeah, I think this is really the key question. I think one of it is already even having a collective effort of serving all the different disparate data that has been generated. Because a lot of it obviously was done under relatively strict time constraints given that there was this ongoing pandemic. So a lot of it hasn't really even been fully integrated. I mean, there have been efforts at already creating some databases, including I think some people also presented already as part of the Global COVID Lab meetings. I think those are useful. But then I think even beyond that, there needs to be specific collaborations between experimental and computational groups. So the data doesn't just get into a database, but there's an actual ongoing effort at integrating this and maybe going back and then testing some of the predictions of these models as well. Right, right.

And I'm just curious, do novel pathogens like SARS-CoV-2, does that alter the sort of T cell receptor domain? I mean, does that sort of make any long-term changes to someone's pattern that you— obviously we're looking at them in terms of age, but prior infections obviously affect that too. And does having sort of a novel pathogen come into the picture, does that change things?

Yeah, I think that's a very interesting question. So we are in the process of, together with collaborators, you know, at UCL trying to have sort of more long-term longitudinal data to see how this one specific exposure at a certain point in time leaves an imprint on the T cell repertoire, say a year after. So we know that for some sort of chronic infections such as CMV, they have a rather big effect. The question is, within that overall large hierarchy, that's something like a mild SARS-CoV-2 infection, like what part of the repertoire does it impact? And also, is there sort of— is it just that everything else is going to go down by whatever it needs in order to still have the same total frequency, or are there some sort of specific clones that might be in competition with these, with the clones that you sort of newly generated, that might go down more than would be suggested purely by a homeostasis of total numbers?

Right, right. Okay, thank you so much. So we have some, some also some specific questions for you about some of your research and your process. One of them is, even though sequence similarity seems to be a key factor, epitopes can be bound by various T cell receptors. So how did you control for this to have a clean clone?

Yes, we actually find both. So we find that within the group of T cells that target the same epitope, there's sort of two kinds of diversity. There's local diversity of T cells that have similar receptors, and then there's sort of a more global diversity where there's T cells that, as far as we can tell, don't have any large degree of sequence similarity, and despite that, they bind the same target. So I think there's structural reasons for that, including that when one actually looks at structural studies of some of these different binding solutions, often there's different structural ways of binding the same target. And so that, I think, is part of what explains the fact that there might be local rules that are very reproducible, but on a global level, there's a high level of ruggedness to the sort of landscape of binding energies and what are the kind of sequences that can bind. And so I think that's an interesting feature of this mapping, and I think we should sort of take that into account as we build these models. Okay.

So we have a question on whether you think a database created from all SARS-CoV-2 T cell responses generated in different studies around the world could help design a universal T-cell vaccine?

One would hope so. I mean, I think part of the question I think that is interesting about the level, for example, of convergence that one sees in these receptors is to what extent are responses public. So how big of a database would you need in order to reliably tell in the context of a certain HLA what fraction of individuals would you expect to have some receptors that can bind that target. But I think the numbers are such that likely for a relatively large fraction of targets, there are actually significant public responses on the level of these clusters of receptors that share a sequence similarity. So hopefully one could pick up on that given the amount of data that we have. Right, right.

So we have another question, which is on the currently available T cell receptor epitope binding data mostly consists of single chain, usually beta chain data, while in reality both the alpha and beta chains are thought to contribute to binding specificity. So what are your thoughts on that?

Yes, we actually looked at both kinds of data, both the single-chain and the pair-chain sequencing data. Indeed, there's a lot more, like the dataset sizes for technical reasons for the single-chain data are much larger than for the pair-chain data. But there is interestingly, even on SARS-CoV-2, for example, a recent paper by Paul Frommer's lab, where there is a significant enough number of paired-chain sequencing data that one can actually do these kind of analysis on. So here, I think it went by very quickly during the talk, but so the upper row here is when one is purely based on single-chain analysis, and the lower lower row here is based on paired-chain data, and one does indeed see that both chains contribute significantly to the overall binding. So the level of enrichment, sort of a quantitative measure of the amount of selection, is much higher in the paired-chain data than in the single-chain data, suggesting that both chains contribute significantly to the binding. But interestingly, if one thinks about this a question of learning the local neighborhood of which neighboring sequences can bind. Even if one only knows one part of the receptor and not the other part, one can still ask what is statistically enriched in the context of having the right kind of other chain with which one would productively bind. So I think we can try and use both kinds of data for this sort of machine learning approach. But clearly at the end of the day, just knowing a single chain and not knowing the other chain means that with most of— say you just know the beta chain, that means that with most possible alpha chains you would actually not be specific.

Okay. So we also had a question that the performance of unseen epitope models is currently still limited by the lack of sufficient amounts of diverse T cell receptor epitope pairs? And do you think there are any appropriate modeling approaches to alleviate this to a small degree?

Yeah, I mean, I think given the kind of analysis that we did, I'm actually skeptical that we're going to get to fully unseen epitope models. Without any experimental input anytime soon, meaning that you give me a peptide MHC sequence and I tell you these are the T cells that bind. And the reason for that is what I alluded to earlier, which is that there seems to be these multiple solutions that actually look very different, and it seems very hard to think about ways of predicting that sort of up-initiative without any experimental input. I think where we really can make progress is you know a few sequences experimentally and then you're trying to predict what are the other sequences that would also bind. I think that we can really make progress on. And at the same time, in experiments where you don't have any information about specificity, for example longitudinal sequencing data, you can look at what are the clusters of receptors that come up that fulfill this kind of patterns that we would expect from antigen-specific clusters. And then really try and refine those and find from there a lot of data at groups of cells that target some epitope that we can then later figure out which one it might be.

Okay, okay. And we had one last question on the sort of redundancy in the datasets where many epitopes are either identical or very similar. And what's your advice for making sure that redundancy is taken into account when people are reporting their data.

Yeah, yeah. I mean, here we sort of been quite conservative about it. We removed overlapping or even partially overlapping peptides when we were trying to do comparisons across different groups of receptors just to really get at what is universal, even if the two peptides are completely distinct. And I think that's important because otherwise you get false confidence in how well you're doing just because you have this sort of leakage between, for example, if you do a training and test set split and you have peptides that are very similar to each other, you might you might get into trouble. So I think my advice would be to remove, at least in the first step, really make sure to remove those. And I think we're now at dataset sizes where you can actually do that and still have sufficient data to do something interesting.

Right, right, right, right. So I guess the last question I have is, tell us about where you are in the process of setting up your lab. And in case anybody's on the webinar who's interested in in joining your type of group?

Yeah, I mean, I definitely— I'm sort of only have been in London for 2 weeks, so things are still very much in the process of getting set up. But definitely one of the reasons I was excited about today's talk is that I'm looking for collaborators at all levels. So I hope that if anyone listens to this and feels that this kind of work is fascinating, that they can write me an email at firstname.lastname@ucl.ac.uk. Or you can also find me on Twitter, AndyMScience, and reach out and get in touch.

Great. Well, thank you so much. I mean, as you said, it is a really exciting time to be doing this type of work and setting up this lab. And I really, really appreciate your taking the time amidst all of that to come and present your exciting work in this area. So thank you so much, Andreas. It's really— it was really an excellent presentation. And thank you also to all of our attendees for participating in today's webinar.

Thank you very much again for having me.

Yes. Yes, thank you. And thank you for all the questions you submitted for our speaker. And I would just like to say, if you're interested in more research on COVID-19, please sign up for the HVP COVID report. A biweekly newsletter that provides insights from experts around the globe and highlights the latest scientific articles and data. And finally, please visit our website and follow us on LinkedIn, where the full webinar series is available, including a video of today's presentation, and where we will also be announcing an exciting lineup of future lab meetings. And with that, I'll say thank you again for participating today. Stay safe, and we'll hope to see you again at the next Global COVID Lab meeting. Thank you so much.