 Hi everyone. I want to thank the organizer for this very nice opportunity to present my work. Thank you very much. And then I've been said I encourage people to ask questions also during the talk if they have anything urgent. So I think today about the concepts of universal dynamics in the microbiological system. But first, before I get into this topic, I want to present how this is related to the big topic of data science or big data. And within the many, the variety of topics related to data science, we can define some maybe a class of problems, of topics that in my point of view are more related to physics. And I tell you why those those topics relate to problems where the data where the data recorded is related to some underlying dynamics to be more specific. When we have usually when we have in this class of problem, we have complex systems, complex systems, we usually mean systems that are systems that are composed of many components that interact with each other. And the data that we can record. This is what we call the system state. This is the activity of the of those different elements. I presented in a general way later on we will speak specifically about the problem of microbial ecosystems, but in general we have a system composed of many elements and we can record their activity. And we can record the system state in different in different states. Now the, the special thing about this class of problem that I want to talk about that we believe that the activity of the element is determined by some underlying dynamics, usually can be graphically represented as a network, the network here mean that each the activity of each element of each component is controlled is affected by interactions with other with other elements and the whole dynamics can be summarized graphically as a network and the general statement behind any any complex system that is an underlying network of interaction and the special thing in this class of problem that we are, we are very interested, very interested in understanding the network. Because if we know the network, we may control the system, we can have a better a better understanding of the system, but the network is usually not available to us. So what's available is the recorded data of the elements. So this, this gap that we have that's that we only only record only the activity of the elements but actually we are interested in the underlying network. This is the something very interesting and this is the big challenge in those type of system. Specifically, I would I would like to focus on the on the system of the microbial microbial ecosystems and specifically the human microbiome microbiome the ecological community of microbial species that live in and on our body in different in different body type that we have them over our skin. In our mouse in the airway, but then the majority of them live in a in our guts. Regarding the numbers of a microbe we it is estimated that the same number of of human cells in our body. And they are classified for into different species now the number of different species depend on what resolution you count them this is in ecology you can you can come them in the different definition you can count the number of genome number of species but so generally as a rough approximation we we are talking in the gut about several hundreds of different of different microbial system. And, but they're the competition that we will see later on is a very personal life. I will think about it later on the general challenge in the the topics is how much can we can we test, can we apply mathematical rules. Precise mathematical rules for those for those microbial ecosystems how much they are there follow some some rules that we can, we can understand and we can define and we can study. And everybody said this is not a this is not an easy question as a very brief introduction to what is the kind of data that we are talking about. So, regarding the guts and the gut microbiome, the, the measurement of the microbial community start with a stool sample and then followed by high throughput DNA sequencing. At the end, we have the abundance profile, so we are mostly interested at the, at the bottom line the abundance profile, this means that for each for each individual for each subject, we can have a list of all of all the species that are present in in his gut. And what, and what is the abundance. So, in this simplified, simplified color bar, we can, we can, so this simplified color bar represent for four different species, the blue, the orange, the yellow, the purple, and different abundances. It is important to note that we only that using this this approach we can only know the relative abundance so we can say that like the blue, the blue species is present in about 50% of the population and so on. This, this, this information is available for each for each individual subject. What kind of data is available to us in general so we have, we have in general to two types of, of data sets. One is called cross sectional data and one is the time period data, cross sectional data that means that we have one sample from each subject, but we have, but we have it from, for many subjects in, in a, in common, large data sets we expect between, let's say about 100, 200 individuals, and for each one of them we have the, their abundance profile. Another type of, of data that is much, much more, more hard to find is the time period data, time period data that means that the same subject is measured daily. So here in this, in the, in the data plotted on the right, each, each vertical bar represent a daily sample from the same, from the same subject and we have it over time or over some period of time. Now this, this kind of data is, is much more real, we have only few, few, few data sets on this kind of data and later on I will show you two of them and you will understand also why. Okay, so any questions regarding just the data and what are we talking about up to now? Up to now there is not, there is not any question, so I assume it's everything, everything is clear. Okay, let's move on. Why we care about the microbiome? Because there are many reasons, the microbiome is very, in general, is very important to, to our, to our health and well-being. Those, those microbial communities they protect us from invasion of, of pathogens, they, they immune, they train our immune system and, and they found to be related to many, to many health functions and unbalanced microbial communities are found to be associated with many diseases. In some cases, even, even the abundance of single bacterial species can be related to some, to some, some phenotype, for example, maybe this, in this cartoon, maybe the green, the green species is related to some, to some phenotype and if we have a high abundance of this green species so you feel good regarding any, any specific phenotype and our main motivation in this, in this study for my, my point of view is ultimately to be able to, to control the microbiome, to, if I, if I have some unbalanced microbiome, whatever this means we will talk about it. And, and I want to, to change my microbiome, so what I have to do, I have to take probiotics, I have to change my diet, what can be done to, to change my microbiome if I want to have some healthy microbiome, to change my microbiome community, what do I have to do? In order to do this, we, we need to understand the, the rules that, that underlie those microbial, microbial communities. So this, so this is definitely our main motivation in those, in all these studies. Okay, some, some basic observations that we have from large studies. Large studies of the, of the microbiome, we have, I will mention here three, three insights that, that I found the physicists that they are very, very interesting and maybe not so, not so trivial. So first is that our microbiome is highly personalized, highly personalized in two features. First, the collection of species, the, the assembly to species is very personalized. And I think that it's, that, that we do, we do not share the same, the same set of species of species. Each one of us has a very, very unique set of species, and when I say, when I talk about the set of species or the assemblage of species, I mean, the presence, presence, absence profile, which, these species are present in my gut. So we, this list is highly unique, but not only the, the, the sets of presence species, but also their abundance is very different as I have suggested by this, this figure, each, vertical bar represent different species and those, and those colors represent their relative abundance of those species and, and all those species, all those subjects are all young and healthy. And, but, but we, we have a large, large variability in their, in their abundance profile. So this actually raise also a general question. I mean, if the microbiome is so important for our health, maybe we would expect to have some, some, some healthy microbiome. And now the data suggests that if there is this kind of concept of healthy microbiome is very flexible, I mean, the, the, there is, there is a large subject to subject variability. So one very general observation. The other observation is that if we, if we now focus on the, on time theory of data of two, of two subjects, we have here subject A and subject B, and these maybe the two longest, I think the two longest available time series data of the microbiome. And each, again, each vertical bar represent a daily, a daily sample from the same subject. So we have a almost one year from subject A and also a more than a year from a subject B. And can be seen from, from this data, the microbiome is very, very, very stable, very stable. So there are, there are those daily fluctuations, but if you just take it, if I just show you one, one random sample, you can easily tell me if this is related to subject A or subject B. So those, those, those daily fluctuations are much smaller compared to the inter subject variability. So, so in general, we can see here that the microbiome is very stable in, in timescales of months and some studies suggested even years. So this is, this is a completely non-trivial regarding the, if you consider the, the, the high complexity of this, of the system and immediately we can think about what, what makes those, these systems so stable. It's very non-trivial. Now, if we, if you look a little bit closer to those time series, we can see that in both subjects, there are some special events here in subject A around the day 100. We may see those green species that appear and also in subject B, there is, there is another special period, a few days where the microbiome is considerably different. And it turns out that those, those exceptions, they relate to, to some special events, specific events that happen to those, to those subjects, some very strong perturbations. In one case, it was that, that's the subject traveled from, from the US to India and probably changes diet or were exposed to different set of, of species. Interestingly, when this guy came back to the US, his microbiome was shifted back to the same states it was, it was before. Now, in the other case, the subject has a diarrhea and he also took antibiotics and this definitely changed his microbiome. But after he recovered from the, from this area, his microbiome was shifted to another, another steady state and stay stable until the end of the, of the measurement period. As can, as can be seen also in this, in this presentation, this is just a PCI presentation of the same, of the same data shown above. And each point represents the daily sample, the, the blue points represent the, the period before the perturbation, the red doing the perturbation and the green after the perturbation. You see, subject A, during the perturbation, this is the time he traveled to some upstate, to India. His microbiome was, was shifted to some other state, but after he came back to the US, he was shifted again to the same steady state, as can be graphically seen here. And that's for subject A, but for subject B, after the, after the perturbation shown in red, he was shifted to some new steady state. So, so this, this, if you summarize this, that means the microbiome is very interesting. Each one of us has a unique, a unique microbiome. And those are, those microbiome are very stable, something keep them, keep them stable. But after perturbation, it, it can be shifted back to exactly the same state or to other, other steady states. Another, another example is the, is those two, two subjects that were treated by FMT, I will not, I will not speak too much about this because the next speaker will depend on it. But what you can see that the, the state of the, of the microbiome was shifted to Dave immediately after the FMT, FMT, the fecal microbiome transplant treatment. And this is a big perturbation to the microbiome. But after, after the, after the few days, just few days after the, the perturbation, the microbiome stabile in the, in some new steady state. And so all these data sets suggests that the microbiome is highly personal life, very stable and also alterable. We, we have a physicist, we, all those featured, we, we immediately think about them as a, we can think about it as some, some complex system in a steady state that can, can be shifted. In small, after small perturbation, the system stay near the same steady state, but if the, if the perturbation is large enough, the system can be shifted to some other steady state. So we can definitely start to think about the microbiome as a complex, complex system. Sorry to interrupt. So there is a question related to the point. So the question is the following. Is there a relatively stable input flow of microbiome species to the human body, for example, through diet. So I guess he's asking what is the role of immigration. So the short, the short answer is that extreme diet clearly affect our microbiome. That means if I start to eat only meat for one week, it will definitely affect my microbiome. But small perturbation, it's, it's hard to, it's hard to see how, how does the other small, small diet change affect the microbiome. So this is the very short, this is the very short answer for this. Okay, so let's, let's move on. As we said that, that those, the abundance of the microbiome, what, what, what control the, the, what determine the abundance of the microbiome. So we think about interactions with, with the, with the host, with the gut environment and also with other species. Those interactions can be graphically represented as a network of, of a, of interaction. Now this network of interaction, this is also kind of, this is definitely a big simplification of the, of the reality, the reality is very, very complex. The interaction, the species, species interactions can be very complex and also the host species interaction can be very complicated through some mediating component and so on. But nevertheless, we can, we can think about a simplified picture of, of the, of this dynamics. In this picture, we say that the green, green links represent a positive interaction between, if we have more from a higher abundance from, from one species this encourage the growth of, of the, of the other species and red, red arrows, red links represent the opposite. All this, all those interaction together and I remind you again that we are talking about a network with, let's say, hundreds of different, of different microbial species, all this very complex network at the end determine what, what's going to be the steady state of the, of the system. So we said before that, that we know that our microbiome is very different, we have different species and different abundance. Now, the question that's immediately asked, can be asked, can be raised is, do we have the ecological network? Do we have, can we speak about one, one network, one unique network that we need to, to find, or maybe each one of us has a different, different networks, different ecological network. Now, why, why should we have different ecological network after all, let's say that the species are the same species. Why, why, why, why, how can we have a different network? So the, the reason that those, those networks are just the outcome, as I said before, those networks just outcome of a very complex biochemical interaction that are definitely affected by very specific factors, such as genetics, or a specific immune system, maybe diet, as was also raised before, and lifestyle, all those host, host specific factors and other may, may lead to very different ecological, very different and very personalized ecological networks. I would like to skip those, those slides to get right into, into the point. So the point that we actually asked you, do we have, what do we think best represents the reality, the case of, of individual, individual ecological, ecological networks, individualized dynamics, or maybe we can, we can speak about some, maybe you can think about some universal, universal dynamics, universal network, one network for, for all of us, I mean, let's say for all healthy, or the majority of the, of the healthy population. How can it be that we have, I mean, if it's reasonable that we have one network, but still, we have a such different microbiome. So the answer is yes, because as we know from, from, from a complex system, that complex system in the complex system, we have this concept of multi stability. So definitely we can, in such, in such complex system with hundreds of species and potentially many thousands of, of interaction, the concept of multi stability can, can be very relevant. Why do we care if we have a universal dynamics or individual dynamics, so as I said before, if we want to, to be able to suggest some treatment to control the microbiome, we need to understand the rules. If we, if we have the same, if all of us or most of us have more or less the same, the same universal dynamics, then, then, then we, we can try to, to infer this, this network and to understand it and to, and to design some treatments. However, if each of us, each one of us have very different dynamics with very different interaction, that means that one treatment that was very beneficial to my friend may be very bad for me because I have different, different rule. So, so this is very, very fundamental question. But when we search the, briefly when we search the literature, we can find some opposite opinions about it. Some, some, some studies really believe or seems that they believe in one, in one network for all and they try to infer this, the network. But other, other studies try to infer it individually and here they try to infer for two subjects and they, they prevent completely different networks. If you decide of the, of those, of those nodes, represent the abundance, but the arrows, if you look closely, you find that they are very, very different. So it is very unclear, even in the literature, what, what is, what should we expect. So that was a question. So I'll do this method work in the sense that you often you have more species than samples so you, you, you cannot infer all the pairwise interaction between species just looking at you don't have enough data to infer this network. So this is exactly the challenge. Yeah, exactly. So, ideally, ideally, if we have enough data, we would be happy. I mean, this would be the ideal approach to straightforward approach was to infer the network for each individual and then to, to compare the result to see if they are similar or not. But unfortunately, as you say, we do not have the enough data to do this. So then we, we should then then we had to find some, some other other approach to address this question. And, and the approach that we, we suggested, we call it the, the, the similarity of a lot of analysis. This means very briefly that we, we compare. We take, we take set of samples. And we compare all, all possible pairs, each time we take two, two individuals and compare the microbiome. And when we compare the microbiome we do it regarding those two different features. First, we measure the overlap. The overlap, the mean, how much the set of species is similar. If they have exactly the same set of species, the overlap is one. If they have no overlap, no overlapping species, the overlap is zero and anything in between. And this is on the Y axis and on the X axis. On the Y axis, we measure the dissimilarity. The dissimilarity is a, actually there are many, many types of dissimilarity measures. It doesn't matter if you can choose any one of them. And, sorry. And then, and you measure how much the abundance profile is similar. We have, we have a prediction. Our prediction is that if the, the reality, if the dynamics are completely individualized, they are completely independent, then the this, this red line, the red line, the red line is the line that represents the cloud of points. This cloud of points is each point here you present the comparison between two individuals. Now, when we do it for the, for the cohort of, of samples from a group of individual group of subjects, then we have a cloud of points. And the red line is maybe the, the, the general trend of this cloud. And our prediction is that if, if the dynamics are completely individualized, then this, this red curve, we call it DOC, dissimilarity overlap curve should be flat. Why? This means that even, even if the, the overlap, even if we have two samples with very high overlap, they've been exactly the same set of pieces, the abundance profile will not, will not be more similar because anyway, the dynamics are not the same. However, in the case of universal dynamics, we have the expectation of this, this pattern of negative slope, this negative slope in the, in the range of a, of I overlap that means that the more the species, the set of species are the same. I mean the higher the overlap is, then the similarity become lower. I mean that if the dissimilarity becomes lower, that means that the abundance profile becomes more and more similar. And this is, this is like a footstep of, of universal dynamics. As you see in our time, I will, I will skip those, those details, these are the details of the, the, the mathematical definition of the overlap and the, of the dissimilarity, we chose the RJFD, but it's, it can be done for any other dissimilarity measure. The, the, the, the main important, I will not demonstrate too much, but the main important, the main important point here is that dissimilarity is defined only over the shared species. And when you do this, the dissimilarity and overlap measure become mathematically independent. That means that they, you can change any one of them independently. However, if, if we do see some kind of relation between them, this can suggest some biological relation between the feature. And when we apply this approach for real data from the, from the human microbiome project shown here in on the left with the, with the blue curve. So here we, we applied it for, from a real data of LC individual, LC individual, a 190 LC individual, the gut, we compare, we study, we analyze the gut sample, and we see a very, very clear pattern of negative slope in the range of eye, of eye overlap. This is in marked contract. If we analyze the same data, but after a randomized their abundance, when, after we, we randomized their abundance there, we effectively removed any kind of, of a, of interaction between them. And in this case, the, this curve is indeed flat. However, in the case of the, we analyze the real sample, we see very clearly this pattern of negative slope. And this subject that, that in our gut microbiome, our gut microbiome largely determined by, by a universal underlying network of interaction. So this is really, really good news for, for us when we want to develop some a control strategy. When we applied the same, the same approach to other body sites, so we find also this kind of negative slope also in our mouse cavity. However, in our overall skin, we do not see it. We see it. We see those flat, those flat blue care. That means that our skin microbiome communities are mainly determined by a by non-universal dynamics, probably by external perturbation. Finally, we apply this, this data over, for over 17 subjects that have a CDI infection. This is gut infection. And we, when we apply their we, we apply our method on our data while they are at the, at the disease. So we have this flat, so they don't have this universal ecology. Apparently, in addition to their disease, they also were admitted by antibiotics or their gut was completely missed. However, they were treated by fickle microbiome, microbiome transplant, and they recovered after, after about four days, and we animate the data of the same subjects after they, they are recovered. And we find this pattern, the very clear pattern of the, of the negative slope. That mean that they've suggested that not only, that they, not only they are recovered clinically, they feel better, but also their microbiome start to follow like the normal, the normal ecological roof, the normal dynamics. So to summarize, we had this, this concept of universal dynamics, we had, we, we find it mainly in our gut and on mouse cavity, but not over our skin. And we, we find this, that this universality is lost in, in a CDI subjects, but recovered after FNT treatment. So thank you very much for listening and if there is any time for questions. Thank you very much. I'll applause for everyone. So we have time for, I would say, a couple of questions. So please write them in the Q&A section or in the chat. So I, I have a question myself, so I'll take the chance to ask it while we're waiting for others. So you find that in disease patient and in communities that are strongly perturbed in the skin, you don't have this relation. So does that mean that, I mean, the interpretation is that, for instance, if you have a disease, you don't have these universal dynamics, you can understand correctly. So you can have a dynamics which is different in many different ways. You can be diseased in many different ways. So are you suggesting that then having a disease or having problems is not being in a different, you know, a different attractor but is really a shift in the overall dynamics. Is that the claim? So actually, as I said, in this specific case of the CDI, the situation is that the microbiome is affected not only by the virus but also by the antibiotic treatment that they have been administrated. So it is, actually, I would say, I would say that we mostly, we do not know, generally, and this is the challenge for us to understand in what disease, the dynamics is different or just from other reasons, the microbiome does not follow the the universal dynamics. I would say that in this case of the CDI, we may think about something encouraging that after treatment, after the FMT treatment, so where the problem is solved and it turns out that the dynamic, the microbiome, is pretty normal. Now, this situation might not be applicable to other chronic diseases. In some other chronic diseases, it might be the case that the dynamics is indeed individualized and then the treatment should be also more individualized. So this is a big challenge indeed. Right, thank you very much. So there is actually a question in the chat. So the question is, is it reasonable to think that of individual microbiomes as a piece of land or a forest, where some are good for growing grapes and some are for rice, and then the other question is, there are dominant species. So I guess the question is, yeah, is it reasonable to think if individual microbiome is a piece of land or a forest, where individual people are good for different bacteria to grow. Yeah, yeah, so I would say that it is reasonable, it is related to some kind of big debate in the community regarding the concept of entotypes. I think that this entotype concept means that some, so that healthy individualized can be classified to some small number of entotypes, maybe three different microbiome states that healthy people tend to cluster around. And part of this debate related to what, if there are those kind of entotypes and those kind of cluster, and if there are exist, what was the reason? So one reason could be multi-stability, multi-state states of the same dynamics. However, it could be as suggested in the question that those different people have some different ecological conditions as a suggestion of the forest, land or forest. So I would say that it is reasonable, but the answer is not yet clear. There are a lot to study here. Great, let's say we have time for one last question. So the question is, if you plot a microbiome of patients of different disease on this similarity overlap plot, do you think patients of the same disease would cluster together? Yeah, I just have to say that the question is very good, but the answer is that I don't know. And this is very, very interesting direction that we are working on it to take this tool of the DOC and try to compare different diseases, and also I will just add to the question that it is also challenging to see how much disease microbiome is clustered or can be grouped according to our approach with the LC microbiome. And this would suggest, I mean, someone can have some God disease or some other disease that related or associated with the microbiome, but not necessarily with non-universal dynamics. So this approach of trying to compare between disease subjects and LC subjects or to compare different diseases is really one of the challenges that we are working on right now and this is still in progress. Okay, so I think we are our time is due, so thank you very much for the for the talk and for answering all these interesting questions.