Can I start? Yes, please. So can I start? Yes. Yes. Okay. So, yeah, so welcome everybody. So it's a pleasure to have you all here. So my name is Angelo Rosa. I'm one of the co-organizer of this digital event. Welcome everyone. So just a few words about this event and the organization. So I'm part of the CISA people who organized this event and I'm also the coordinator of the local SECAM node here at CISA. This event is organized in collaboration with ICTP and tomorrow Ali Asanali will tell you a few words about ICTP. So just a few words about SECAM for people who don't know. So SECAM is a big European consortium who is putting together many institutions interested in computation, molecular simulations and is probably one of the biggest consortium in the world. Normally, as a node, we organize such an event each year as a school mostly for undergraduate people. We had the plan to do this year too in collaboration with ICTP. Unfortunately for this COVID crisis was not possible. So we decided to change the event a little bit and organize it as a group of talks online. So it's the first time for me actually to do these things. So please be patient if everything will not be perfect. So again, welcome everyone. We have a very nice list of very, very good people and very good talks. So for this first day, we will give the talk to the organizers. The idea is basically to do seminars which are a bit introductory for the most topical talks of the next days. So in such a way that people who are not familiar with many of the topics, because you have seen that the program is quite broad, would get used to the language and then can follow easily the most specific talks of the next days. I have two advertisements to do. So please switch off the videos in order to save a bandwidth. Okay, so that's good in order to avoid the technical problem. And also a more technical announcement. So the talks are recorded. So if there is someone that does not want to be recorded, just switch off the video and keep the video switch off during the session. So you are allowed to ask questions by raising the hand. And then I will pick you and tell you that you can ask questions. So I don't know for time being is all by my side. I don't know if Fali wants to add something. Yeah, maybe I'll also take this opportunity just to welcome everyone on behalf of ICTP. So I guess all of you know, so ICP is the Abdul Salam International Center for Theoretical Physics. We would have loved to have you all here in Trieste, but unfortunately, this is not going to happen. But you know, we're trying to make do with this virtual medium. We have ICP has a whole bunch of, you know, programs and specific mission to develop capacity, scientific capacity in developing world. I'm not going to go into details here in the beginning of this event. But for those of you who are interested, definitely get in touch with me and be happy to talk to you. So I think we're already running late. So I just hand over to Angelo as the host. Thanks, Fali. And so I think we can just move to Giovanni and to his talk. Okay, so we share screen, right? Okay, so can you see my screen? Okay, good. So good morning to everyone. So my name is Giovanni Bussi. So welcome to everyone. I'm also one of the organizers. And so, yes, as Angelo said, this is an experiment that you are doing. And it's also the first time that I co-organize a virtual event like this one. And actually, it's also the first time that I give a talk to a virtual event like this one. So I hope everything will be with work smoothly. So the idea of my talk is to give you a flavor of what you can do to reconstruct biomolecular dynamics using molecular modeling tools, some molecular dynamics and experimental data. And in particular, I will focus on RNA dynamics, because that's what my group is devoted to. And so at the very beginning of my talk, I will try to convince you, I mean, to tell you why we decided to work on RNA, so why RNA is cool. So if you look at the central dogma of molecular biology, what you learn is that your genome is made of DNA, which is also the information, and then it's copied, it's transcribed into RNA. And then RNA is used, the instructions written on RNA are used to build proteins, which are the real actors in the cell doing all the stuff. But actually, if you look at real numbers, this is only the fate of a very, very small fraction of the genome of complex organisms. And for mammals, in particular, is around 2% of the genome is coding for proteins. But the majority of the genome is coding for RNAs that have then other roles, other functions in the cell. And typically, they have regulatory roles. So there are a lot of RNA molecules whose role is not just to store temporarily genetic information, but they can do much more. And so it's very important to study them. So let me also give you a very short primer on RNA structure just to set up the language. So the RNA structure can be analyzed at three different levels. So you have the primary structure or 1D structure. People call it 1D because you can represent it in one dimension as a string of characters. It tells you the sequence of nucleotides composing the RNA polymer. Then you have secondary structure, which is the list of helices and loops, how they are arranged. Also, which are the nucleotides that are Watson-Crick-Paird and so on. And this is also called the two dimensional structure because it's easy to put it on a piece of paper. But then you know we are not living in flat land and in reality molecules can be arranged in complex three-dimensional structures. And that's what the tertiary structure of RNA is. Okay, then that's the structure. But what about the function? Clearly, the function is related on the structure, but depending on the specific RNA molecule, it could be related to the primary, to the secondary or to the tertiary structure. For instance, if you look at coding RNAs, those whose goal is just to store temporary genetic information, clearly the function is primarily linked to the 1D structure, so to the message stored on the RNA molecule. But if you look at non-coding RNA, the function could depend on the sequence alone, as it is in some case, or on the secondary structure, which basically tells which nucleotides are paired and which are not, so which of them are available for further pairing, or on the tertiary structure, which is the three-dimensional arrangement of the molecule. As I think it's easy to guess, so the three-dimensional shape is particularly important when the function is exerted by interacting with particles, because typically when two molecules interact, they need some kind of complementarity in shape. And in this case, in particular, also dynamics is fundamental, because typically molecules, when they interact each other, they have to rearrange a bit. So clearly for RNAs that are involved in functions, like binding to proteins, to ligands, or doing catalysis and so on, the three-dimensional structure and the three-dimensional dynamics is fundamental. And that's where molecular dynamics comes in. And so molecular dynamics is a really powerful tool that can be used to model, basically, the system of interest at an atomistic scale. So every atom is represented as a point in space. Then you have some function that tells you which is the energy of the system, how it depends on the position of all the atoms. And typically, this energy partly comes from chemical bonds, from angles, from torsional potentials, and so on. You have very, this is a very mature field where people have tried a lot of different forms. So to give you an idea of the kind of applications that we do are typically done using these empirical force fields, where you have interactions that are chemically motivated. You describe the system at atomistic details, so every atom is a point. And we typically include explicit water and ions, even if in many movies I don't show them for clarity. And unfortunately, these models do not take into account any polarization effect. So that means that the charge of each atom is decided a priori, the partial charge of each atom, and it has no way to adjust based on the context. And this is an important limitation. And if you want the extreme case of polarization is charge transfer or chemical reactivity. And that's also out of question with this kind of approach. Okay, so the good thing, that's the bad thing. The good thing is that these models are pretty fast and you can easily run several nanoseconds per day. I would say it depends on the machine that you have and how big is the molecule that you are studying. And as a tool, what we use is Gromax, which is a very popular and free molecular dynamics engine, and Plume, which is a tool to do enhanced sampling simulations that I'm also co-developing, and I will advertise a bit better later. So why do I like molecular dynamics? So I like it because it gives you access to very high resolution to your system with very high resolution and it's virtually unlimited. We can access basically to as short timescale as we like and also to very short length scales, so to the atomic scale. And in addition, we have access to dynamics and it's relatively cheap in the sense that these typically simulations can take a few days or a few weeks, depending on what you have to do. There are also drawbacks and in particular the total timescales that you can access are not as long as you would like in many cases and I will give you more details later on this. And then all the accuracy of your results is related to the fact that the model that you use is reliable. So I discussed already some of the limitations of these so-called force fields and clearly the better the force field, the more faithful will be the result. And then you have to remember that it's still, it's just a model, so it's a way to model your system to learn a lot of stuff, but the most important thing is to compare your results with the reality. And in this sense, I like to quote this sentence by Vijay Pandey that is, in science, as in life, it is very dangerous to fall in love with beautiful models. So we always have to validate our MD simulations against some experiment to have an idea if they really make sense or not. Okay, so the first problem is timescales. So which are the timescales that are relevant for RNA dynamics? So you will find around many pictures like this one in several reviews or papers. This is a picture which is customized for RNA dynamics and where you can see that if you look at very simple dynamics like rotation around bonds, that's easily accessible on the nanosecond timescale. If you want to look at base pair formation and opening, that's more challenging because it reaches the microsecond timescale. And there are other processes like binding of different cations or even switching between different to the structures that are totally out of reach for atomistic molecular dynamics, as you can see in the bar above. And that's why in order to study this kind of process, you really, you cannot just use plain molecular dynamics, but you have to complement it with the enhanced sampling methods. And as I told you for implementing enhanced sampling methods, what we use is a tool called Zoomed. Okay, then there was also an issue that I mentioned with force fields. So what's the state of the art for, so what's the typical level, how accurate are force fields that are used to describe RNA molecules? This is just a bunch of pictures from the literature. I will not go into the details, but you have the reference if you want. These are just studied that so from the group of Hirgis Ponder and Tom Cheetham on tetranucleotides and also from our group on tetradupes. I will just summarize this side is saying that the community is not very much satisfied with the current state of the art of RNA force fields. And there are many things that can be improved and should be improved. There have been recent improvements. I would mention a couple of relevant works, one from the David Shaw group and another from the Hirgis Ponder group published last year, which are improvements, but still I would say that it's really, it's not easy to start the project using molecular dynamics on RNA and be confident that you will be able to reproduce experiments. And so in this year, as soon as I realize this, I switch, I slowly switch it to instead of just comparing with experiments, say using experiments as restraints in my simulations, which is a nice way also to understand the more about how the experiments are done. So which type of experiments would I discuss now for RNA for, so in particularly interesting are experiments that allow you to access dynamics. So that take into account the fact that molecules are not like frozen in a single structure. And in particular, I would like to mention NMR. I'm not an expert of NMR, but to summarize very quickly what you can access with the nuclear magnetic resonance is like distances between atoms, between atoms labelled in some way or torsional angles or other geometric features. There are, there is a really a zoo of different techniques and people that are very specialized in each of them. The way to connect the formulas, the equations to connect the three dimensional structure of a molecule to an experimental signal are kind of established. So it's kind of easy to compare with your simulation with NMR or even to use NMR data as restraints. The only tricky part is related to the fact that NMR experiments are done in solution. This is technically a problem, but it's actually a very great feature because it allows you to access dynamics indeed. But the issue that comes in is that what you are measuring is not the property of a single copy of your molecule, but you are measuring some average over an ensemble of copies of your molecule. And so you have to keep that into account whenever you want to use NMR experiments as restraints for molecular dynamic simulations. Okay, so after this pretty long introduction, this is my optimistic agenda for today. I'm really happy to be interrupted. I'm not sure I will be able to see if people interrupt me, but I guess Angela will be able to see raise the hands and stop me if necessary. And I will be happy not to arrive to the end if I receive too many questions. So just stop me if there's something that it's not clear. So the first part of my talk, I want to show you how we combine experimental data in particular NMR with molecular dynamic simulations. And I will give you a bit of the theory first. And then I will show you how we use these to study a very important non-coding RNA system. And then in the second part, if I can arrive there, I will show you some different way of combining molecular dynamics and experiments. And here I would say molecular dynamics is done in a semi-quantitative way, just to give hints about which experiments to do. And then the real work is actually doing the experiment. And this is something that we published recently. And it's a nice work where we managed to understand a lot of things about RNA and DNA and zipping dynamics. So let's see if I can arrive to that part. Okay, so the first issue is with the average restraints. So this is something on which the community of molecular dynamic simulation has worked a lot in the past 10 or 15 years. So the issue here is that so you have a molecule that can explore a number of different configurations. And whenever you observe something that is an average over these configurations, what you will see in your experiment, in your signal, is like an average over all these conformations weighted with their probability to be observed at P. So that's what you are expected to compare with. And now the problem is that this is a highly undetermined problem. What do I mean? So if you have one observable, so if you measure the average distance between two atoms, there are a huge number of different possible probability distributions for that distance that are all of them compatible with the same experimental value. So in a trivial way, you can say if the average distance between two atoms is five, it could be that the distance is always five angstrom or it's half of the time four and half of the time six. So how can you choose the probability distribution that is more reasonable among the list of all of those that are compatible with experiment? So there is a kind of consensus in the community that the cleanest way to do this is to pick among all these distributions, the one with the largest possible entropy and actually to be more precise with the largest possible relative entropy, relative to a prior decided distribution, which would be the Boltzmann distribution associated with the force field that you are using for your simulation. So in other words, what you say is that your posterior probability is among all of those that agree with experiment that would give you an average equal to the one proposed by the experimenter is the one that is as close as possible to the distribution that you would obtain just running a straightforward MD simulation with your force field. Okay, so how can you do this formally? So if you maximize the entropy and you compute its derivative with respect to the probability and you can do some math and it's easy to show actually that the posterior should be proportional to the prior multiplied by an exponential factor which is e to the minus lambda times and this f is the quantity that you are measuring. So let's say you are measuring the average distance between two atoms. This would be e to the minus lambda times the distance between those two atoms. That's the same as saying that the potential energy should be augmented by a factor by a term that is linearly. It's linear in the quantity that you are observing with a pre-factor lambda and you have to choose this pre-factor and then you have to choose this pre-factor in such a way that the average over the posterior is equal to the experimental average. So this can be done iteratively. You can start with somebody of lambda and then compute the average, compare it with experiment and then adjust it a bit until you have agreement between simulation and experiment. So some more comment on this method, this maximal entropy method. So here in this plot I have like a histogram of some observed quantity and let's say that my force field gives me the red distribution with two peaks, one here and one here with two different weights and the average from the simulation will be some value here and then I go to the experimentaries and it tells me now look the average is here. So if you just add to your system harmonic spring keeping the distance equal to that value you will have just a single peak in the posterior distribution here. If you use max and instead what you will do you will rely on the peaks produced by the force field by the molecular dynamic simulation and just modulate them so increase the weight of one and decrease the weight of the other until the average becomes compatible with experiment. So from this simple example you can see that the amount of information that you retain from the original simulation is much much bigger with respect to just enforcing restraints in a simplest possible way. So you need very good starting point so very good prior distribution and then you need also a lot of data and the more data you have the typically the more reliable will be your result. So what I'm discussing here is max and but there are many closely related approaches in the literature so the group of Michele van Druskolo has used since many years approach based on replicas that is has been shown to be equivalent to this and there is a method from the group of Parinello that was born as an un-set-something method but can be casted also in a maximum entropy framework and experiment directed simulation from leg vault and there are also bahisian methods with very similar formulas and very very similar properties. Okay good so if you look at this maximum entropy based methods you have basically two manners to use them one is to enforce so to use your restraints during the simulation and here you have a problem you you might have got that you have to choose these lambda factors to run your simulation but you don't know the value of priority so you have to adjust these lambdas during the simulation and this is done typically with an iterative procedure that is not straightforward but this allows you to sample the correct conformations during your MD simulation or you can do it up posteriori with the reweighting schemes where what you do is you take your trajectory done with a possibly incorrect force field and then reassign weights to each of the snapshots so that you weight more the snapshots that are more correct let's say but using this maximum entropy framework in such a way that the weighted average on your ensemble will agree with the experiment and okay we have also done together with Max Bonomi and Mikhail Vendrusko a technical work where we compare very the efficiency of these two possible approaches so to make it short so clearly reweighting is really nice because you do it up posteriori so you take your 10 years old simulation or you take your fresh simulation but you're weighted with datasets from 10 different experimental groups and every time it's very cheap because you just have to reanalyze your simulation whereas if you want to enforce your restraints you need to have the experiments before you run the simulation and clearly if the experimental data change you have to run your simulation again okay so I don't know how much time I have yet so I will try I will continue with this nine minutes okay so I think I will only show the first part I try to go though to be kind of didactical on this part so I will show you this application now so this is an application of this maximal entropy based method on a non-coding RNA this is a sign B2 element that was identified in the group of Stefano Gustincic at CISA some years ago so this is a antisense RNA that is used to enhance is used by the cells to enhance the gene expression so it basically finds a complementary messenger RNA binds to it and then enhance its capability to produce proteins by a significant factor and the nice thing is that the experimental group working on this was able to identify so they managed to identify first this element here which is a 100 and something or almost 200 nucleotides with this function but now they are coming out with the idea that this herping alone is able to to trigger this function and so we decided to try to study the dynamics of this herping to have an idea of which are the structures that this herping could have so what we did or actually what the experimenters did they did NMR experiments first NOEs which means that you measure pairwise distances between protons and you know which pairs of protons are close which pairs of protons are far or on average let's say and then what the experimenters typically do they try to build a single structure that satisfies all these restraints all these constraints so if two protons should be close to each other yes that should be close full stop and then if you try to enforce all these signals at the same time you so I you can guess that could there could be some trouble because this signal could come from a mixture of different structures so now if you look at the PDB that was solved using this experimental data it contains 10 structures it's shown here but basically can be grouped in the like structures equivalent to this one and structures equivalent to this one with a small tilt in this nuclear base okay so the first thing that we try to do we took these structures which are experimentally refined and try to run MD and the first thing that we see is that so the first structure agrees with all the experiment we run MD for a while and suddenly we don't have agreement with experiment anymore so the first thing that you might think is okay that's because your MD simulation is total crap so you have a wrong force field the system starts from the correct configuration but goes into the into an incorrect one that's actually not the case if you look at the structures it's it's not too difficult to to realize this and in particular so here in this plot what I'm showing is the distance that is measured between a specific purse of proton and this the guy the glycosidic bond angle is the the rotation around the bond that connects the nuclear base with the sugar which has some typical distribution that should be around here then if so what if we take our MD simulations and then we use reweighting in order to assign a high weight to those frames that agree with the experiment let's say and experiment tells me that the distance should be smaller than this horizontal line then I will add a lot of weight to points which are here but these points are in the tail of the distribution if you look at the structure visually you will see immediately that these structures are incorrect they are really stressed so in order to have this distance to be in agreement with experiment you make your nuclear base very very stretched you put it on the tail of the Gaussian and this already suggests you that something should happen actually what you can expect is that in reality there is a mixture of this structure and of another structure that is completely different but once averaged correctly with this one would give you the the experimental observation okay so in order to see this this torsional this rotation of torsional angles you need an anset sampling so here we used some variant of metodynamics and replica exchange that if you want you can find in the paper the details and during the simulation we we also for this the agreement with these experiments we we see dynamics and and then if when we analyze with the same metric as before our simulation we see that from time to time so some of the structures goes to a different rotamer where the where this torsional angle is flipped to a sin conformation which is expected to be rare but not impossible and indeed that's able to explain the experiment without the need to resort to a very uncomfortable position for the nuclear base okay so how can we then rationalize our results so at the end of a max end procedure what you have is an ensemble you have a lot of structures but you would like them to be not too many not thousands because you don't you don't want to watch thousand structures so the first thing we did is a clustering analysis and also we Sabina riser who was the the post of working on this project worked a lot in doing these cool pictures so this tells you basically the how heterogeneous is the ensemble that you expect to exist and to be in agreement with the experiment but okay there are so there is one important comment about this clustering because we struggled a bit on doing clustering correctly here what we wanted are clusters that are really homogeneous structurally so with basically the same NMR signals and the structure which are similar to each other and standard clustering methods do not have this feature and so what we did we we decided to use a homemade very expensive method based on maximum clicks that work pretty well but there is a very nice paper published this year by Gonzalez Aleman et al where they actually show that the quality threshold clustering which is a method published in the 90s can be used very effectively to obtain exactly these so clusters that are structurally homogeneous and that's not true with the some of the methods that are used very much in the literature as it's explained in this really nice paper cited here okay so still okay we have clusters but there are too many I really don't want to watch all of them so Sabina Reiser had the idea of trying to use a combined maximum entropy with maximum parsimony so let's try to instead of using all the structures that we have let's say let's try to only use structures coming from one cluster can we reproduce the experiment the answer is not so let's try to use structures from two clusters three clusters and so on and what she discovered is that for this specific system what you need is four clusters which due to the way we define them they are different from each other and so they contain structures with different annotations and different base pairs and stacking patterns and with this specific population so the answer is not unique you have different possible sets of four structures but the nice thing is that you can really find out which are the structural features that are required to reproduce experiments so you can see that you need some of this guanine to be in a synconformation and you need some of these AU base pairs to be broken and that's very interesting because for this we have kind of independent validation we have other experiments that we did not use in in this calculation that suggests that these pairing AU here are at least transiently not formed so I would say this is a kind of independent validation of our result yeah okay so just summarizing these okay this okay I will not summarize let me just make a small advertisement so if you are interested in learning more about enhanced sampling methods we are organizing plume masterclasses and I think Max Bonhomme will tell you more about this at his talk there will be zoom lectures with a limited number of participants the participants will interact through a slack workspace and the deadline for application is soon is in a couple of months and okay now let me jump to the very end of my talk just to show you the pictures of the people that did the job so this is an old group picture but I needed this because this is the work the work that I showed was made by a poster that now left my group with Sabine Reiser who is here and then I want to thank also the experimental collaborators for the work that I show you that are Stefan Augustincić and Silvia Zucchelli who disappeared last year and then thank you all of you for your attention thank you very much Giovanni I send you also my reaction and so yes so questions so as I said if you want to make a question so just raise your hand and then I will reveal which of your audio so there is a thank you very much from Davide Bassani don't be shy yeah don't be shy just thanks a lot can't find there is your end may I speak sure yes this is Shravani from India hi hi nice to be in ICTP after a long time so I have a question very nice talk I just needed to understand I do see in the literature not only maximum entropy but also maximum caliber models so what is the difference between the two okay so maximum entropy is for ensemble averages maximum caliber is for a dynamical trajectory so in a nutshell it's a it's the same but instead of being applied to averaging between conformations it's applied to averaging between trajectories so again if I have a non-ergodic system then only there will be a difference in the two predictions. Ergodic systems it should not matter right if I have long enough sampling. I'm not sure this is a correct interpretation so the point is that with the maximum entropy what you obtain is ensemble averages but you don't obtain time correlations now let's say that you have an experiment that measures the time correlation function of an observable then you can use the maximum caliber in order to enforce that time correlation function in your simulation so it's like the difference between enforcing an ensemble average and enforcing some time dependent ensemble average as it would be a time correlation function so it's really I would say it's related to the kind of experiments that you use not on the effect on the ergodic of the system. Okay okay and I have a second question if you know the rate constant of a given associated with some some kind of a conformational fluctuation in the kind of systems that you are talking about so which enforcement is going to be more appropriate. If you know rate constants I would say you you cannot use maximum entropy you have to use maximum caliber or in other words maximum caliber is just it's nothing less than from my understanding nothing less than maximum entropy applied to trajectories so but you have to use maximum caliber to enforce rate. Okay, thank you very much. Giovanni there is a question by Sharon Arti. Is it possible to use the experimental restraints to then refine the force field? Yes it is possible so this maximum entropy framework is not designed to do that because the correction to the force field is going to be by construction the one that changes the least the distribution so as I said if you are measuring a distance you will correct directly that distance whereas when you want to refine a force field typically you choose a priority based on some other chemical intuition the functional form let's say you want a force field made with torsional angles and then you can refine those torsional angles in order to get agreement with experiment but that's not within the maximum entropy framework because you will not maximize entropy anymore you will maximize agreement with experiment directly I don't know if I answer to your question. Other questions? Are there more questions? Questions? I can't see any. Yeah, don't be shy ask questions. Well okay I don't know if there are none I think we can thank Giovanni again for the talk. It's time to you and so I will stop sharing now. Then I think we can move to Edgar. Yes can you hear me? Hello. Yeah we can hear you Edgar yes. Okay very nice one second let me try to share screen. Right, do you see my screen? Yes we do. One second more. Do you see my pointer? Do you see my pointer? No. Ah yes yes. The right thing okay. Yeah yeah. Yes the right dot. Exactly. Okay okay. Go on. Okay so welcome everybody I'm one of the co-organizers of this online activity. I want to thank the other co-organizers especially to Angelo who took care of a lot of work for this to happen. As Ali said before I also work in STP so it's a pity we cannot meet in person but okay we can do what we can do at this moment and I would like to invite everyone who has questions to make questions during my talk especially young people because we're going to discuss about stochastic thermodynamics which is not the main topic of this of this event so there will be a lot of new concepts for many of you and in particular I will discuss on something we call martingale which is a tool used in finance that we are using in the recent years to explain fluctuations of thermodynamic systems like the ones sorry to interrupt there is a small window in the middle of your slide. A small what? There is a like a small gray window that that is overlapping on your slide I don't know it's written no big defects. Do you see it now? Or maybe just move down okay. Okay okay. Well let me start with a review of thermodynamics this is what it's in many textbooks and classical thermodynamics so the first law says that you can get something for nothing so energy is illustrated with this stone is transforming to two different forms of energy one is heat that is dissipated in the surroundings and the other is called work that is used to to move things like this bucket you have here. The second law on the other side it discusses the irreversibility of thermodynamic processes and it says a few words that you can't even break even meaning that as I showed here in this with this glass you can processes tend to increase the disorder of the system or of their environment following this law so you can in general the entropy of a system increases meaning it becomes more disorder and also the entropy of the environment so you can make a system more organized by reducing the system so the system entropy reduces but there is a price that this you have to pay this price heat dissipated to the environment which increases the entropy of the of the surroundings right so in the recent years there has been a lot of progress in doing thermodynamics of smaller systems like for example a DNA herping a colloidal particle or a nano electronic system here I show an illustration of a colloidal particle that is driven out of equilibrium because there is an external force pushing the particle but it's a small particle so it's a bit of fluctuations. I'm also an organizer of the this activity and I want to also thank Angelo of course he made a lot of work for making that this work and thank you all for being here I'm going to talk about a topic that it's somehow transversal to all the Alex that we are going to be clustering technique clustering is some supervised machine maybe we have to change the speaker that deduce the... Okay, can someone mute Alex? Without using it in a priori classification. Okay, all fine. Can you hear me? Yes, so sorry there was probably a misunderstanding. All right, let me go on. So I was talking about this particle moving right and left with fluctuations, which is a typical example of stochastic thermodynamics. So we do thermodynamics with few degrees of freedom. For example, we aim to understand what is the heat dissipated by the particle when tracing a particular trajectory. This type of formalism was introduced in the 98 by Kenseki Modo, who by the way will be giving a talk in this activity. And he introduced a formalism to describe what is the heat along a single trajectory or what is the work along a single trajectory of the particle. So these are new concepts developed in the last two decades. And there's also the concept of stochastic entropy production, to which I will discuss in detail in this talk. And there's a second law, which is now for ensembles of trajectories. So you can have a trajectory of the particle going against the force, and this is interpreted as a negative stochastic entropy. But on average, the particles, if you look at many trajectories, they will move more towards the right and towards the left, because there is a bias. So we'll go into this in more detail later. This is a typical example of a model that we study in stochastic thermodynamics. So we have a chemical reaction, reacting some products. We have different chemical potentials. And thermodynamics tells you that you will have a flux in the direction of the gradient of the chemical potential. So you will have, for example, this reaction happening in this direction. In stochastic thermodynamics, we say everything can happen. So we assume that all reactions and the time reversals can happen with different rates. And a key assumption in our field is that the rate of a process and of the time reversed is related by what is called the environment entropy produced along one of these transitions. So this is for one transition. But as I was telling you, you can look at a particle that is drawing a long trajectory so that you will have many transitions. So when you collect these many transitions, you can build probabilities of trajectories given an initial state and probabilities of the time reversal trajectory given a final state. If you take the assumption of the equation I gave you before, these two will be related by the environment entropy change along this trajectory. Similarly, you can do the same with the system entropy. This is not the Shannon entropy, but it's the stochastic version of Shannon. It's just the logarithm of the probability to be in a site extinct at Antti. There is still this technical issue with your slide. On the screen, it appears like a small gray window on top of your presentation, on the top right corner. Yeah, let me try to... I'm closing everything I have open in my computer, so... Yeah, because otherwise it goes on top of the formulas, then we don't see things. Yeah, I don't see anything. Is it fine now? No, it's still there. I mean, I don't know. It's written no build effects. I don't know. No, it's group. It looks like something. What are you using? I'm using keynote as always. It looks like something. Edgar, right now, there's something on the right called build order. Can you close that? Okay, give me one second. This is the animation panel in... All right. I guess now it's fine, no? Okay, thank you. Sorry. All right, so this is the definition of the fluctuating system entropy, and if you sum this entropy plus this entropy, you get what we call stochastic entropy production, which becomes the Boltzmann constant times the logarithm of a full trajectory divided by the probability to see the time reversal trajectory. So this is a measure of time irreversibility of a process. And we often write it like this, so the total entropy associated to a given trajectory is the logarithm of the probability to see the trajectory divided by the time reverse probability, so the probability to see the time reversal trajectory. This is a formula that we use in stochastic thermodynamics to study irreversibility of different processes. Here are examples of systems that are paradigmatic. For example, is we have a periodic potential with an external force. We say this is a non-equilibrium, but this steady state. So this is an external force that is time independent. So we are not changing the Hamiltonian in time, but there is an external force pushing the particle, so such that it has a net current. But there are more complicated modes. For example, Feynman-Ratchets with two thermal watts or active matter, which is attracting a lot of attention in the last years. So stochastic entropy production has some universal properties. One is that if your system is in equilibrium, it doesn't fluctuate. It is always equal to zero. So its average is equal to zero. But the most interesting part comes out of equilibrium. So out of equilibrium, this is a fluctuating quantity, and it can even be negative. You can have an experiment where the particle is climbing a potential, and this we interpret as a negative stochastic entropy. But on average, when you average over many experiments, you will have always a growing curve. This has been seen also in experiments, and you can see negative entropy in electronic experiments that we will discuss later. So in the last years, there has been a lot of research on finding universal results for entropy production, work, heat, etc.  So in principle, it is because you just have to measure probabilities and trajectories. You don't need to know anything about the physics below. But if you take a physical system like an electrical circuit, you can measure the net growth of this stochastic entropy, and you see it's related to the heat dissipated in the resistor in this experiment, for example. And as fluctuation theorems, as I said, these are theorems. These are relations that are universal. They are common for many physical systems. And one is a very important one is the detailed fluctuation relation shown here that says that at a given time t, it is more likely to see positive entropy than negative entropy by this relation, which implies the so-called Yashinsky equation. All these are fixed time properties looking at your system at a given time. But I was interested in the last years in finding other type of new properties for which there was not much known. For example, the random time. So what is the first passage time of entropy production? How long it takes to produce one KBT? Or what is the extreme value of entropy production? We say it's negative. It can be negative. So how negative can it be? And these have obviously important consequences for, for example, schematic reactions, which we know that happen at fluctuating times. Or in polymerization processes where you can have backtracking events and this extreme entropy could be related to the extreme excursion of a motor. I will discuss about this in a way. So this is also to motivate anything. And maybe now go to the key concept in this talk, which are martingales. These are processes used in probability theory, also in gambling and finance. And they have interesting mathematical properties because they provide a shortcut to tackle extreme values next stopping times. So we can have tricks to calculate extreme values in an easy way. And they have been surprisingly unexplored in stochastic thermodynamics until this paper and also our work which started a new research line on thermodynamics with martens. So it's very surprising because they appeared in all the books in probability theory gambling and finance, but there was no link to such a strong link in physics until recently. What is a martingale? So martingale is a process that we say a martingale with respect to xt is a real value function. This is a real process that is bounded. And the most important thing is this condition here. So if you know x from time zero to time s, this is a martingale with respect to x, what you expect in the future is the last observed value of the process. So it's a process that has no drift. For example, Brownian motion is a martingale and fair financial markets are market or fair games. To give you an idea, this is an illustration. So you look at the process and you know the history up to time tau. If the process is a martingale, what you expect anytime in the future is that its average value is exactly at the last observed value. This is what this means. So it's a process without drift. All right. And this has been applied very much in finance. So let me ask the following question. Can a gambler make fortune in a fair game by quitting at an intelligently chosen moment? So you have a process and you say, okay, for example, this will be the money I have in the stock market. And I say, okay, I want to win. So all I need to do is wait until this process reaches good benefit. I don't know, 10,000 euros, for example. You just wait. So you would make profit out of this axon. However, the problem is we have finite money. So at some point you will enter, if you have Brownian motion, Brownian motion can go infinitely low. So you can get infinite losses. So you would make profit, but this is not possible in gambling or in finance. However, you would say, okay, I want to win. I want to stop if I get 10 euros as a revenue or if I'm losing five euros. So I do a two boundary first-party problem and I win. It turns out that if you have a martingale, by doing this, there is no combination of thresholds by which you will win. So at the end, at the stopping time, the average of the process is the same as at the initial time. So on average, the gambler makes no profit. So you cannot make profit with martingales. This is the main message. So a gambler cannot make fortune if it cannot foresee the future and it has access to a finite budget. So this means it's using a stopping time. You cannot see the future. And second, it has a finite budget, is uniformly integral. So this is a bit technical, but mainly there was this theorem by Dubb that says if you have a martingale, what you expect at the stopping time is the initial one. This is called Dubb's optional stopping theorem. And it's valid for any stopping time, not only a two boundary first-party problem. Okay, this is a very powerful result, true for all stopping times. So this is a big class of first-party times, let's say. And we found in 2017 that there is one property of entropy production that is martingale. First of all, we found that entropy production itself is a so-called sub-martingale. So you have this condition. If you know the past, you know that in the future it will grow given any previous knowledge. And this implies the second law, because if you put tau to zero, you know nothing, so it implies the second law. This came from finding that exponential of minus the entropy is a martingale. So it has no drift. But we have this condition that I'm trying to show you, this one. It's a martingale. And this, if you set tau to zero, this implies it's a k-quant. So it's very nice. This looks a bit mathematical, but this opens up because you can take a book of martingales and look at the mathematical properties and apply them to physics. And this was what we did next. So we applied properties, mathematical properties of martingales to get into these stopping times and the extreme values of entropy production. So in the stopping times, we found applying the martingale theory, very surprising results. One was that if you put two absorbing boundaries and you measure the time it takes to reach the top and the bottom boundary, you will have more hits in the top than in the bottom boundary. But the time it takes, so the distributions look the same. The histogram has more counts, but the shape is the same. So there is a symmetry in how long it takes to produce entropy production. There is this symmetry for the times, which was for us extremely surprising. So you are going in this direction more than in here. But given that you reach the boundary, you take the same time to reach the top boundary with a drift than to reach the negative bound. So this was a very surprising symmetry that we could test with an experiment. So you have the particle here, you put a boundary here and a boundary here. And of course, it will fall down because you are pushing the particle more. But if you measure the time to reach the boundary in the bottom and the top, they are the same. They are the same distributions. And this is a new result that we found using martingales. Moreover, we applied this theorem that I told you that you don't gain with martingales to entropy production. And we have now a fluctuation theorem at random times. So any gambling strategy that you use, you will have no gain for e to the minus s. You will have a gain for s because you apply Jensen inequality and you get there is a second law at stopping times. And this is for any gambling strategy. You can put two boundaries and the boundaries, you can put them in any positions you want. It's a very, very, very general result. Right. And this is an illustration. So in a fluctuation theorem, you have systems in a non-equivalent steady state and you wait for some time. You let them evolve, let them evolve dynamically up to a given time and you collect the entropy at the final time, the entropy production. And if you sum them, it's positive. Now we say something else. We say we put a criterion. So we put, for example, a ring and we track the systems until they cross this ring. This is a random times. Each system crosses at the different time and we measure the entropy production at this crossing time and there is a second law even in this. The nice thing is, sorry, that this one is a particular case of this one because one specific stopping time could be you have your clock and you wait until your clock ticks three seconds. So it's generalizing the previous results. Right. And now I think this is even more exciting, our extreme values. So we are looking at what is the negative record of entropy production. You look at entropy production to a given time and you'd like to know what is the negative record? What was the minimum value in a finite time? With Martin, as we can calculate the statistics of, we call this infimum. Because there is a theorem by Dupe, well by Jampil, because he is totally from him, which tells you the distribution of the maximum of a supremum is bounded by its average at the final time. You can apply this to entropy production and get these very nice results. The first is a bound on the full distribution of the minimum. And the second is that the average minimum cannot be below minus one constant. So there is a lower bound, fundamental lower bound for the mean of entropy production on average. And this is very, very general. So these mathematical results, you can take a theorem and see what are the assumptions of the theorem. These assumptions become conditioned for the physical process. It's a value for Markov chains, for Langevin and Amis, for continuous time, microprocess in a steady state. It's a very general result. It's so general that we went to a lab and tried to test this in an experiment. This was a condensed matter experiment. It's an electronic double dot. So we have two islands and they are electrons. This is a very low temperature. Electrons that can tunnel to these islands. The electrons see each other and they have a Coulombry person. So all in all, this behaves like a four state system in which either you have no electrons, you have one electron on the right, you have one electron on the left, or you have two electrons populating the islands. In this system, you can measure entropy production, stochastic entropy production for different biases. You bias very strongly in the system. This grows very fast. And from here, from this trajectory, measure these extreme values. And it turns out, measuring the extreme values and building the distributions that our theory is really good. It's really providing a bound to the extreme excursions, the distribution. And then, if you do the average, the average minimum, a very long trajectory, cannot be below this bound we found, the minus one bound for the infimum. You get closer when you are closer to equilibrium, 25 microvolts. When you drive strongly the system, you don't saturate to minus one. And this is something we applied later in biophysics. So now, let me go a bit more on the topic of the conference, which is an application to biophysics. So we use this theory of extreme values to relate molecular motor fluctuations with random matrix theory. This is a surprising result derived by my student, Alexander Giet. We were looking at a simple model of a molecular motor. So we just have a walker that walks to the right for jump rate K plus and backwards with jump rate K minus. And this is in periodic boundary conditions. The time is continuous, but the space is discrete. We define here A is a cycle affinity is the bias parameter, which is related to the force, net force applied to the motor, the length and KBT. And there is also a symmetric parameter it's called rate that appears as a pre-factor in the two rates. This is a simple model. So in principle, one should be able to calculate everything analytically here. The nice thing is, if this is in a ring, all states have the same free energy, this one, this one, this one. You have a uniform distribution in the ring. So the entropy production becomes just the work. And this is FL times X, simple. And therefore, the entropy production in this model is proportional to the position of the motor at time t proportional. This is not general, but it is a simple example to illustrate our results. All right. So this means that when you jump with the drift, you dissipate heat. So you produce entropy. And when you jump backwards, you are reducing it. So it's like you have a particle rolling in a linear potential. And when you roll down, you dissipate heat, you roll up, because you are taking energy from somewhere, from above. The question we wanted to address is the trajectory of the motor, single trajectory. We look at what is the running minimum, what is the minimum up to time t, and the running maximum. We'd like to understand what are the statistics of the running maximum and of the running minimum, and also of the running maximum of the entropy production and of the running minimum of the entropy price. These are important in biology in general, because to understand robustness and resilience in biological systems, which are subject to failure, like for example, there's here a micro tool that is an extreme event in which the polynomial, it starts to enter in catastrophe or sperm navigation is an extreme event as well. So we think that understanding resilience and robustness is important in biology, not only averages. So the first thing we could derive in this model is the long time extrema. What is the long time minimum of the position of the worker? And first of all, we find this is the distribution of the minimum, it's a geometric distribution. And second, the average minimum has this expression, so it only depends on the bias parameters. And when A is zero, this goes to minus infinity. So at the stall force, the extreme value diverges. The average extreme value, which is this line diverges. However, this doesn't happen with entry production. This entry process is A times this. So what happens is the following, that this is bounded. It's not bounded by minus infinity, it's one minus the both one constant, sorry, which is what we show in the previous work actually. So when you make the bias stronger and stronger, the long time minimum gets closer and closer to zero. When you're close to the equilibrium, you are here. So more importantly is that not only we can see the average long time values, which are here, here, but that my student could derive a very nice expression for the full curve, the finite time average minimum, which is given by this formula. It looks a bit scary, but I'll show you a very nice way of expressing this formula. So the main point is we found there is a symmetry, mean maximetry, between the minimum of entry production, this excursion, and the maximum. So this is the value of time t minus the maximum at the same statistics as the minimum. And this is related by this formula. Interestingly, we found that this formula can be rewritten as an integral over times. This is like a relaxation spectrum, and where the relaxation spectrum is given by the so-called Marchenko-Pastur distribution. This distribution has a finite spectrum. It has this asymmetric shape. This is called Marchenko-Pastur, and it appears interestingly in random matrix theory. So it turns out the following, that if you want to calculate the extreme value, you can do a very nice shortcut. You draw a random matrix. So this is a matrix, which is size m times n, and its entries are random numbers. And they can come from Gaussian random numbers, for example, with a given rectangularity. So the size, the asymmetry in the size is related to the asymmetry in the bias of the walker. So you plug in random numbers in this matrix, and you construct a wishart matrix. So you multiply the matrix by the transpose, and you divide by the number of columns. Then you diagonalize the matrix with the eigenvalues, and it turns out that if you make this sum, exponential of minus t divided by this eigenvalues, this gives you the average meaning. The matrix, yes, you have three more meanings. Okay, fine, fine. I have more stuff, but I'll summarize some. All right, so it turns out that you can compute very efficiently extreme values of the molecular motor by drawing very small random matrices. And this is what we show here. The black line is the exact calculation, and the points, for example, is taking a four by four matrix, just one matrix, making the eigenvalues, and making the sum. This gives you this very nice approximation to the extreme value. So we got very excited about this result, and we are trying to fully understand it because it's a surprising connection to us. I don't have much more time just to tell you very briefly, these ideas can be applied to more complicated models, where you have a spatial coordinate, and a chemical coordinate, for example, ATP consumption, and the position of the motor, and okay, I don't have much time, but recently, very, very recently, we introduced what is called gambling demons. They are different to the Maxwell demon. It's illustrated here. It's a demon that is gambling. So you can either stop the process at a fixed time, or stop when it has gotten a very good revenue. So it means it is using, okay, this work is done by Gonzalo Manzano here at ICTP. You can stop, for example, the work at a given time, only if the work didn't cross a given threshold. So this is similar to what I was telling before on the stopping times, but now with driving, before it was steady state, now that it's driving. And okay, I finished soon. It's just that we derive this second law, work minus free energy at the stopping time. It's not greater than zero, but it's greater than something else. If you have a question we can discuss in the discussion tomorrow, which is related to the asymmetry of the process. And we could find in an experiment that you can go below the free energy by doing these gambling techniques. This we could see very well recently in an experiment. The more irreversible you are, the more you can gamble, and more you can go far from the second law. This is very interesting. You can see this in our archive. Okay, just to finish, Martin is in the air. So there are different authors that are following this approach. Here are good examples. Kerskeimoto would give a talk about it in this activity. We are writing a review. I put here to be finished in 2050 because it's taking us a long time to finish. And I want to thank you for your attention and also to different collaborators on my current team for the great work. So thanks a lot. Thank you very much, Edgar. So as before, we are open to questions. As before, don't be shy. Yes, even if the question is a concept or anything, please go ahead. So maybe I'll just start to break the answer. On this last part, Edgar, sorry. I didn't understand what is this delta. I just missed it. So this is, okay, one second. The delta is information theoretic quantity, which is the logarithm of the ratio of this is the density at time t in the forward process. And this is the density in the backward process because here it's not a steady state. So it's a driven process. So you drive the process from time zero to time t and you look at the snapshot at a given time. This one is the same snapshot in the backward process. So you are looking at the density of the process in the same time, but in the forward on the backward process. So this is the density. For example, there is a process that goes from time zero to time 10. And this would be the density at time two in the forward process. And this is the density at time eight in the backward process. Okay. So it's a measure of the things diverge. Yeah. So this is the forward process. And sorry, one question. You start from zero. You start from zero and you finish in town. So you're looking at a given time in the forward process. Sorry, my drawing. The forward process is flowing in this direction. And the backward process will flow like this in this direction. So you are looking here at this time in the backward process here. Forward and backward. When the process is very reversible, the statistics of the process here in the forward process will be different than the statistics of the process in the backward at the same time instance. So this is measuring the density of x at time t, this one. So this one is here. And this one, I'm just messing up the colors, but this one is here. So this measuring the probability to be given x at a given instance in the forward and the backward process. When you are in equilibrium, they are the same. But when you are out of equilibrium, the driving processes generate asymmetries in the distributions. So that's why we are calling stochastic distinguishability. Distinguishability in the forward and the backward process. Thank you. So I see that we have a hand raised by Marcelo Albuquerque. Please. Okay, thank you. Thanks for the talk, Professor. Nice talk. My question is about the bias in the system. I don't know if you understood what you said previously, but you said that the system, I don't know if you would be biased or if it could be biased. I would like to understand. So this could be, for example, a motor pumped by ATP and there is a chemical reaction that is, and there is an asymmetry. For example, here, there is a potential here that is asymmetric and there is a force ATP that is pushing the motor more in one direction than in the other. In the way we describe, this can be anything. So this is a net force on the motor. For example, there could be someone pulling from the motor. For example, you can have a motor in an optical tweezer and you can pull from the motor in the optical tweezer. This means there is a bias. So the motor is going, walking more in one direction than the other. It has transport. Okay. Thanks. So we will have to to take into account the force that you are putting. Yes. Okay. Yes. Thanks very much. All the models I discussed have a bias. They are non-equivalent. Okay. Thanks. Excuse me. I have a question. You mentioned about microtovols in bonus slide. I don't remember. Could you please explain more, because my work is about microtovols and so please explain more. Yes. Of course. Thank you. Yeah. So here, the model I take is a motor that moves forward and backwards step-wise. So this is a forward step. This is a backward step. And the motor is biased. So it makes more forward steps and backwards. And I'm interested in looking in this process, the black one, what is the maximum of the process? What is the running maximum? Or what is the running minimum? So the blue process is what is the minimum up to this time? If there is a minimum now, the process goes below, the minimum has changed. This is like the record, I don't know, records in athletics. So this was the shortest time. But now there's a new athlete that has a shorter time. So this goes down. Right. So we are looking at records in stochastic process. This one is stochastic. In microtool, these type of events, downtrends are very important because you can build that trajectory with the length of the microtool. So now I'm not looking at what is the motor. I'm looking at what is the tip of the microtool. When it grows, this goes up. And when it shrinks or has a catastrophe, the length will decrease. Okay. So all in all, you have a process that is doing like this, fluctuations, like the black process here. So here, the extreme values are very important because negative extreme values are catastrophic events. So if the extreme goes very, very low, here is catastrophic because it means the process will, the microtool will be dislodged fully. So I think there is a lot of room for application of our results that are general. Two of these modes can be applied as well. Thank you very much. Are there questions? Yes. Sorry, I have one more question myself. So regarding this model, you said that this is discreet in space, but continuous in time. Why is it continuous? Is it not just a random walk? This is a bias random walk in a lattice in continuous time. Yes. Yeah, why is it continuous in time? Is not, because if you're in some kind of... Well, I assume time is continuous always. And I put discreet space because it's a coarse graining. Yes. But so mainly what we are doing in this time series is a Gillespie algorithm. So we run at random time until the next step. But this is a good description, I think, for single molecule experiments when you can distinguish states in the model. Of course, let me just say one thing more. Of course, it is more precise to me to have something like this. Like you have your motor here and you can either do a displacement via mechanical force. You can consume ATP without moving, which would be this. Or you can consume ATP and move, which would be this event. So using discreet, to me, the best model is continuous space, continuous time. But using this type of approach with discreet is useful when in an experiment you can only see parts of the dynamics. You can see only coarse grained states of the system. But I would take that continuous time because I think it makes more sense. So we have another question from Catherine Azizi. So please. You showed some graphs on the entropy evolution in time, which was decreasing. So I was curious, is it for the isolated systems? Or is there any entanglement effect? Or is it just so that it is isolated? Yes, this is a good point. Here the description that we do in stochastic thermodynamics is something more similar to what you see here in one second in this figure. This is the paradigmatic model. So we have a colloidal particle. It's the gray particle. This is in a potential. It's this black line. So this is the colloidal particle. It is in a potential. There is an external force. And there is a bath. I'm not putting the bath molecules here, but this is full of other particles, green particles that are around that are interacting with this particle. So I'm not talking about an isolated system. Of course, all together will be an isolated system, but we look at the dynamics of only of this guy, which you can describe by this type of model. It's a long given dynamics where there is a bath, which is this noisy term. In other words, I think it was better this one. We are doing thermodynamics on this colloid. But this is the entropy that we look is the entropy exchange between this colloid and the environment, not of the full field. It's a classical system. It is canonical. It is in a thermal bath. It is not an isolated system. Of course, to do this simulation, you need to isolate the box, but in stochastic thermodynamics, we just see this red particle. We don't see the others. We want to do thermodynamics on the trajectory of the red particle. So we look at the entropy of individual particles, and then we will see some decreasing. No, no. This, yeah, yeah. It decreases because this particle is moving backwards. So we live in the world of land-driven dynamics. We live in this world. For us, this is what is our world. So in this world, you can have events where the particle climbs up, and this is because it's absorbing heat from the environment. But we are not tracking the heat exchange with each individual particle, but we are living in this description, which is noise, the noise accounts for an average force of the bath molecules. So it's an effective description. It's a mesoscopic description, what we do. Thank you very much. I think we stop here. Thank you, Edgar, for the very nice talk. And so I think now we move to Alessandro. Hi. Okay. Alessandro, you can just go on. I can share the screen. All right. Fine. So. Okay, great. Please tell me if you can see my presentation. Yes, we do. All right. Great. So my name is Alessandro Laio. I'm also working in CISA. I have been working for quite a while on the development of advanced sampling techniques, even if more recently I am more focused on data analysis and data science tools, also for analyzing biomolecular systems. But, okay, today I will give you an overview of, well, not of advanced samplings in general, because this would require five days at least. But at least on the reason why advanced sampling is necessary. Okay. So, well, our dream as scientists, well, let's say my dream as scientists, everybody can have his own dream, but, okay, one of my dreams as scientists is actually has always been trying to understand from a physicist's point of view how biomolecules work. So these things, biomolecules are amazingly interesting machines, which actually are extremely efficient. They do incredibly precise tasks based on what? Based on the laws of nature, of course. So they basically convert thermal fluctuations into ordered work in a manner which is absolutely amazing, and we would like to be able to copy in order to, well, for example, design nanomachines. So this thing is understanding really how biomolecules are working is actually a big challenge for nowadays science. And, well, molecular dynamics has been and is going to be one of the key tools for addressing this extremely important challenge. Okay, so what is molecular dynamics? We have already heard a lot about in the talk by Giovanni. So given a potential energy surface, one solves new consequences of motion. So very, very easy in principle. But in order to make it efficient, you need a lot of work, a lot of ideas. So basically, nowadays, modern molecular dynamics tools, codes are extremely efficient, are parallel and is scalable. So these, these required a lot of work, a lot of work with more than three decades of work by, well, not really hundreds, but I would better say thousands of people. So nowadays, the molecular dynamics tool that we have in our hands are extremely powerful. We have to understand where the first thing we're going to understand the first part of my talk is how powerful they are. So why is it necessary to have powerful codes? Because if I want to simulate a realistic system, for example, a realistic biomolecule, I have to cope with three different problems, the different codes. So one is that I would like to, to simulate large and inhomogeneous systems. Yeah, this is the image of a membrane channel, for example. So this is like 300,000 atoms easily. Well, then I have a problem with the time scale. This is the one on which I will dedicate a little bit of time in this presentation. And the other issue is the accuracy. You know, one would like to have from these simulations a quantitative answer, not only a nice movie or a qualitative description, but really something that helps you to understand how, for example, a biomolecule is working and eventually adapt it in such a way that you can, for instance, control its behavior, right? So here in order to do this, you need accuracy. So here you have to choose the correct level of accuracy for performing your simulations. Here, in this overview, I will simply start from there, because this is actually the key point which will then determine how much time we can simulate. So which level of accuracy of description should one choose? So this clearly strongly depends on what you want to simulate. So, well, let's say the chip option is using classical potentials. If you use a classical potentials, of course, you will not be able to describe a chemical reaction, but you can really, really do a lot. You can already study how, for example, a protein works, how a protein, a typical protein, not an enzyme is able to perform its task. So here there are no quantum effects on atomic motion, no electrons, no chemistry. Well, what we call a force field is a potential energy function and a set of parameters which enter in its definition. It is designed to reproduce the molecular geometry and some selected properties of the molecule. Also, in order to develop these force fields, these required really, really a lot of work and a lot of insight. It's a, now almost a four decades old story. So here, just to give you an idea, so this is the functional form of a potential energy function for performing biomolecular simulations. You have a bond term, an angle term, this one. Then we have a dihedral term which describes the interaction between four successive atoms. And then, well, and then we have the non-bonded part, which is actually the rate-limiting part. So here computing the first part is somehow cheap because it involves only the few atoms which are close by. Instead, computing the second part is what makes the computation expensive. Okay, so here then you have another option. Let's say that you want to describe a chemical reaction, then you have to deal with the electrons. So if you want to deal with the electrons, you have to go and chat a little bit with Mr. Terschrodinger and use his well-known equation. Okay, then in principle, you would like not only to solve the electronic structure for a given configuration, but also do dynamics using the forces that are derived from your electronic structure. Then you want to use at the same time the Schrodinger equation and the Newton's equation, and the manner of using these things together was actually first developed and invented here in Sissa by Carparinello in their famous 85 work. Okay, so this approach is great because variance with a classical force field like the one that I described in my previous slides does not require any fritting, no free parameters. Everything comes from first principle, but of course you pay a price. And this price is basically it is orders and orders of magnitude more expensive than the classical force field. So orders and orders of magnitude. Okay, so here now this is an important slide because it gives you a little bit an idea of what we can force simulate in now a day. So let's start with the classical force field. So let's make an example, a simulation of HIV protease with a classical potential. So this system has approximately 50,000 atoms. Okay, so each atom interacts approximately with 100 atoms. Let's say it's neighbors. So in order to compute the forces in a given configuration, I need to do something that basically I need to compute forces between 50,000 times 100 atoms. So in order to perform this number of calculations and ordinary CPU, a single ordinary CPU needs to do basically this can be done in approximately 0.2 seconds. So in 0.2 seconds I compute the forces, all the forces on this system and then I am able to move my system for one step. So here basically in one day I can move the system well here basically you can read the calculation is very simple but basically half a million times. I can move it half a million times. So this means that I move my system half a million times by a time step. This time step is if you know a little bit about molecular dynamics is one tenth of a second which means that in one day I will be able to basically simulate one nanosecond, one nanosecond in one day. One would say so this is already this is an enormous technological success if you compare to what we were able to simulate decades ago but it's only one nanosecond in one day. So here this is what we can do with classical potential if I want to use a carparinel or a quantum potential in which electrons are treated explicitly. What I can actually simulate is something much smaller. I can simulate a much smaller system and instead of 10 to the minus 9 seconds I can simulate only 10 to the minus 11 seconds. Well of course I can use something which is much better than one single CPU and people across the world have built large computers. In particular David Shaw in New York City has built a computer which is able to do only molecular dynamics of proteins. So this gives you an idea of how important this task is. So he has invested an enormous amount of money so this is the money that he has invested 100 million dollars of his own money. So this guy decided to invest his own money in order to make this thing work and he has built an hardware which is able to do only this. So of course it is much faster than our computers of course. So what can you do with that? So with that you can simulate 17 microseconds per day on a system more or less of the size that I mentioned in my previous slide. So 50,000 volts. Okay so this is an enormous technological advantage and in fact these guys are obtaining amazingly good results using these fantastic computers. But how far can we go with these numbers? Okay so let's say that I am rich and therefore I have this computer so I can simulate 10 to the minus three seconds in one month. One millisecond. So this number 10 years ago would have looked like a miracle science fiction. So let's say that here with my resources I am able to simulate instead 10 to the minus five seconds in a month. So two orders of money to last but still quite a lot. But now okay so the typical time scales of interesting transitions are typically orders of money to longer. So even protein folding. One millisecond there are many many proteins which in order to fold take almost a second. So this means that we are even if I have this enormously powerful computer I will not be able really to see even a single folding event in many many proteins of great interest. The situation is even worse if I want to simulate phase transitions. Phase transitions happen on mesoscopic time scales. We are used to see phase transition happening in our real world time which means seconds hours. So how can I simulate a phase transition if I am only able to simulate one millisecond? I have a problem. Abination is even worse. Chemical reactions also chemical reactions. There are many chemical reactions which happen on the time scales of minutes hours days. So these things are clearly out of reach for direct molecular dynamics simulations. Okay however even with the moderate computational resources we can do something. I'm going to show you two examples which are well both not from my lab. So this is a simulation of the folding of a knotted protein of 86 amino acids which in real life falls in approximately 0.1 seconds. So 100 times longer than what it is possible to simulate with the big computer which I mentioned. So this is the folding trajectory which was obtained well in the lab of Pietro Faccioli in Trepto. So it's possible to obtain this thing and it's possible to obtain many folding trajectories like that. First example. So this is a second example a phase transition in the zeolite. So this system in order to form to observe a phase transition like that. So this is something which in real life happens on the time scale of minutes if I remember correctly. So here already more than 10 years ago it was possible to obtain and observe systematically and study systematically many phase transitions of this system with moderate computational resources. So here you see a trajectory with the system really jumps from one phase to another. How is this possible? How is this possible? Well the key for making this possible are enhanced sampling techniques. Here of course in the 20 minutes that I left in my presentation I don't have really a chance to give you even an overview of everything that is around but at least I would like to leave you with the idea of what is the gist, what is the main thing that makes this miracle possible. So how is it possible to pass from well a simulation that is 10 to the minus 8 seconds to get information on a process which would occur in on the scale of seconds. How is it possible? All right well let's try to give a close look to the systems which we already mentioned. So the idea is to understand a little bit what's going on. We should first of all find the function of the coordinates which is likely based on our chemical and physical intuition to take very different values in the different states. We call this function S of X. So here for example in the case of phase transition a good function is the box shape. Here you see that in this transition the box simulation box changes shape. Here in a chemical reaction the bonding pattern here you see that these atoms form different bonds in the different states. Here in the case of protein folding I can choose many the fraction of alpha helix, the number of contacts, the gyration radius. So I have to find the function which basically takes different values in my different states. Okay now how would this function behave as a function of time? Okay so this is an example here this is a very simple system. Here I have a simulation time and here I have my collected variable. Here you see that I have a fluctuation in one state and then a jump to another state. Okay so here so this is the time before observing the reaction. So this is the time which is of the order for example of seconds or hours or of days and this is the reaction time. Here you cannot even almost see but it's actually much much shorter than this time before the reaction. When we say that protein folding of this knotted protein of course on the time scale of 0.1 second we are actually talking about the time before the reaction not about the time that the reaction takes to happen. So this difference this subtle difference between these two things is actually our handle where what we use in order to develop power and unsamplified techniques. So how do we do it? So in a molecular dynamic simulation of a chemical reaction if a transition the system actually spends most of the time oscillating in a local minimum. So this is actually the key point. Only rarely it performs a jump to another state. The time required to perform the jump is short. It's very very short. For example in a chemical reaction you can have a waiting time of one hour but then the time that the reaction of course to really happen as soon as it starts happening can be one picosecond 10 to the minus 12 seconds. So one hour so waiting time with nothing happening and then 10 to the minus 12 seconds everything happens all of a sudden. So the key trick which is at the basis of all the enhancement technique is finding a manner to simulate only the jump. So this is actually the key trick. Then all the different methods work in different manners but this is the key trick of the business. Okay how do I do this? Here I can do it well in many different manners. Here as I said in order really to give you even a hint on all the different manners I would take hours. But okay one idea is to pull the collective variable s. So once you have found that your system is nicely described by a specific order parameter for example something which describes the order of your structure then you can simply add a spring on this specific variable and simply pull it like exactly you would pull a spring and force this collective variable to change. So this is the idea which is at the basis of the thermodynamic integration which is a very well known method and also steered molecular dynamics. Then you can do something which is more rigorous which is a well I like to call it important sampling on reactive trajectory exactly like you do important sampling on configurations when you do Monte Carlo you can actually devise a sampling scheme which preferentially sample only reactive trajectories. So the most famous approach in the field is transition for sampling but actually there are other methods which are also related with this idea of simulating only the reactive part of the trajectory for example the finite temperature strain the nudge elastic band in the framework of the chemistry. Then okay another idea where which I will actually describe in a little bit more detail is the idea of flattening the free energy here I will spend the next few slides on that so I'm not going to tell you anything on that at the moment. And then another idea is to rise the temperature so of course if you rise the temperature your rare event become less rare but you cannot simply trivially rise the temperature of everything otherwise you simply melt the system and transform it into an ideal gas which is not very interesting. So you have to rise the temperature in a smart manner and you can do it in many different manners. One manner is temperature-accelerated molecular dynamics where you rise the temperature only of the collective variable only of S or you can rise only the temperature of the solid. It's called solid temperature. So all of these approaches have their own history their own advantages and disadvantages. Now I'm going to spend the last part of my presentation in describing a little bit more what it means flattening the free energy. So what is the free energy first of all? So here this is the trajectory that we were looking at before. From this trajectory what you can compute is the probability density. You can estimate the probability density as a function of your collective variable S and it will look like that. You will have a maximum here and another maximum here. This maximum corresponds to this state and this maximum corresponds to this state here. So from the probability density you compute you define your free energy. Your free energy F as a function of S is just minus KBT the logarithm of the probability density. So here if this is the probability density this is the free energy. So a minimum in the free energy corresponds to a maximum in the probability density and so in this specific system you will have a free energy which looks exactly like that with two separate minima. So here what does it mean flattening the free energy? So let's say that I start with this free energy here. If I do my simulation on a system with this free energy I observe a trajectory like that. Long waiting time and then only few transitions in this time that I am able to simulate. Then they say that I add to this free energy an external bias. So the external bias here is in this specific example which I'm going to show this weird form which is a sum of two exponentials. So the sum of the free energy plus my external bias would be this red line here. So you see is flat. Now if I simulate my system under the action of my normal potential which has this free energy here plus this external bias what I get is this trajectory here is the same system but now you see that the system is going up and down again and again and again. So this thing is actually making exactly what I was telling you before. So adding this bias allows me to simulate only the jump only the jumps but now and so therefore instead of wasting all my simulation time waiting for the system to vibrate and then for a very rare event which happens only from time to time I force the system to go back and forth again and again and this allows me to observe many many times the relevant transition. Okay so here this is great. This was actually invented in the 70s and it works great but well we have a problem and the problem is who gives us this fantastic bias potential which is able to flatten at least approximately my free energy because of course when I start my simulation I don't know how the free energy looks like right so this. So Alessandro sir you have four more minutes yeah why pardon four more minutes four more minutes yes but I am almost ready okay so how can one find a bias potential b of s which is approximately equal to minus the free energy and which therefore when added to the free energy give me something which is approximately flat. So here so I have many many options which were all used again and again and again across the years well first of all is using my chemical or physical knowledge to invent a correct bias potential option number one option number two simulations with simpler potentials I simulate it with a cheaper potential I compute the free energy and then I define my bias using this previous simulation so the other option is an automatic procedure I'm going in the last three minutes give you some hints on a possible automatic procedure which is called metadynamics so in metadynamics the bias potential flattening the free energy is built iteratively by an approach which consists in a loop described in this two lines here you basically put a small Gaussian and then you evolve the system for a short while under the dynamics of the small Gaussian plus the free energy so first you add one Gaussian and you go there then you got another one and you go there you go there you go there and you go there so basically this idea of adding from time to time a small Gaussian actually actually is a procedure which allows you to iteratively flat flatten your free energy and iteratively build a bias which compensates your underlying free energy so more rigorously you choose a collective variable s of x and you bias the dynamics with a historically dependent potential which has this form here here we have an example of the free energy which is at the beginning unknown plus the sum of these Gaussians which iteratively become more and more flat so here I have the sum of my free energy plus the bias potential defined by this equation which is flat which actually means that for large time my bias potential defined by this equation here is an approximation of minus the free energy okay so here is an example of a normal molecular dynamics and metadynamics applied on a system undergoing a chemical reaction which in a normal carparinello molecular dynamics would be absolutely impossible to simulate and here well and this is well really I am finishing yeah maybe with this movie where still you see nothing happening for the moment but now all of a sudden you see that the guy is able finally to do some stuff and performing a list a sequence of transitions in which the system actually jumps from one free energy minimum to the next and well exploring the conformational space in a very efficient manner so here you see that now now the system is actually performing a transition to a molecule which is called naphthalene so it's almost gone and now it goes to naphthalene we wait another second yes we wait okay now it's gone now it's naphthalene and with this okay well here of course I could show you other examples on systems more interesting systems on which we have applied these things we have studied many many systems with these approaches for example the folding free energy landscapes of a protein or the the free energy landscape associated to the nucleation of fibrils here yeah here I would show you many many examples but actually I would like to close with a slide where I show what in my opinion are the open problems where which are still at the center of the research well not only for this specific method but for many many methods so the first important problem is how to find automatically the best collective variables here here if you don't if your system is very complicated it's very difficult to to know in advance what is the best variable on which you should add your bias or pull your simulation or rise your temperature so this is the first important problem a second important problem is that using these powerful and unsampling approaches you actually observe many transitions you are actually able to explore very complex conformational landscape and an open research topic at the moment is how can I analyze automatically these complex conformational landscapes so both these two problems actually call for a combined approach using machine learning artificial intelligence and data science tools so this is basically well the reason why I personally more and more you trying to use approaches from this thing simply because they give you tools which allow you to address this problem which otherwise with classical method would be more difficult to address well with this I'm finishing my presentation and thank you very much for your kind protection thank you very much Alessandro for the very nice talk and so as usual now we are open to question let's see if in chat okay yeah there is hi can I ask a question yeah sure oh who is he I'm Uriel Morson yeah sorry yeah just for the question please raise your hand otherwise I cannot see sorry I don't know now go on please okay okay thank you Alessandro it was very interesting and this is a very naive question I don't know much about these methods but it's like two questions in one one is does the meta dynamics preserves the statistics like ensemble statistics like a canonical ensemble or I mean are you violating that or is it important to preserve it or not so if I can answer immediately this is a very important question it is not in the sense that it is a dynamics which basically basically adds a history dependent potential to your system therefore therefore the probability distribution of the system is of course not anymore canonical but during the years many people have done a lot of work and it is now this probability distribution is actually now very well understood and even if it's not canonical in the initial variable of the system basically people are now able to extract the original probability distribution original canonical distribution as doing basically a post-processing of the biased probability distribution so the answer is yes this dynamics perturbs the probability distribution but but there are results which in some conditions are exact results which allow you really to basically compute back the correct probability distribution from your meta dynamics trajectory very nice okay this then this answer my second question was how to obtain the free energy from from this method so well basically from this method is the free energy is naively speaking is minus the bias more rigorously speaking is minus the time average of the bias so basically in meta dynamics the bias becomes a dynamic variable itself is like having another dynamic variable this dynamic variable is a field because it's a function and in order to obtain an estimate of the free energy would take the time average of this bias so this is also not a rigorous answer because the rigorous answer would require having a blackboard and much more time but just to give an idea you take the time average of the bias okay so this is true even if the statistic is not preserved even if the statistic is not preserved this is rigorously true if the dynamics in the collective variable is a diabetically separated from the dynamics your other variables or in the limit of infinitely slow depositions there are technical details thank you very much sorry Alessandro we have a few questions yeah one from denis what collective variables did you use for your study well an enormous amount of collective variables the thing is that this is an art so if you go to plume the plume there is the plugin which implements all the rare event methods including meta dynamics you will find a list I think of 50 collective variables but just to give you an idea you can use like coordination numbers which describe the bonding pattern you can use the energy the energy is a total energy is a very good collective variable you can use the radial distribution function you can use the stress you can use whatever you want any possible function explicit function of your coordinates can be a good collective variable for studying your system so this is where the fun of our work is somehow no it's choosing the correct collective variable for any specific problem yes there is another question by from Lorenzo parlante is asking in your opinion what is the best method to define a realistic transition path between two states and could you recommend some tools or software for biological systems okay so here the most if you really want to define the pathway the transition pathway in a rigorous manner in my opinion the correct tool is transition path sampling the approach developed by in the group of David Chandler Chandler the lago and so on so here so this thing is something which is totally agnostic it doesn't require choosing a collective variable it simply does important sampling in the trajectory space with no prejudice and then you analyze a posterior these reactive trajectories they this group they developed their tools if you browse on the web for their names you will find the tools which allow you to do this thing cleanly so this method on the other hand doesn't allow you really to explore your configuration of space like we are doing in metadynamics is more a tool which if you know reactants and products where the system is going coming this allows you really to allow it rigorously how the system is performing the transition okay so maybe one last question from Alice Romeo she is asking what's the difference with gaussian accelerated md in which you automatically add the boost potential without pre-defining collective variables um well i i think it's so any method so i don't think that what you say is possible in the sense that what you can do is to add a gaussian acting on all the coordinates for example all the dihedral like it is for example done in not adaptive force bias in floating in so i don't remember the name of the approach but okay so but this approach does not allow you to compute the free energy because the bias it is acting on too many variables uh does not really converge because the the size of the space which you are exploring uh depends on the number of variables on which you are put in the bias so if you are biasing if you are simply putting a gaussian on the coordinates then you are biasing a space which has a dimension 30 000 and you will never be able to fill with gaussian 30 000 dimensional space okay yeah sorry i think we uh stop here thank you well of course let me say that if you have other questions you are more than welcome yes exactly to me uh private email or i don't know if we have a public chat associated with this so in any case my mail was on my first slide you can see it on the record if you want okay thank you very much alessandro again so we move to the next speaker and i have to ask you to accept the invitation to the breakout room hello sir can you hear me professor rhodriguez can you hear me yes okay you you can start the test please okay shall i start uh sharing my video yes can you see me okay and then my my screen can you see that yes can you activate the full screen yeah well okay right yes okay okay so we are already streaming so we are ready to start i'm gonna start recording i kindly ask the moderator to tell me if we can start in seven minutes hi can you hear me yes yeah i think it's fine so the only thing is that the first talk will be in the separate room so if the if the third and fourth speakers are already here so arie i think we'll join later yes if angelo is already here maybe we can try his screen sharing oh yes because professor micheletti does not want to be recorded okay right uh but we expect some more participants right we have 30 participants now yeah yeah but uh i mean if the so now we are not in streaming right yes we are in streaming because we are streaming all the day i see in a single block on youtube okay so if angelo is here maybe we can test his connection okay sharing let me check no he's not in yet okay so i think we can wait a few minutes and then uh around two maybe if angelo and adi didn't show up yet we will move to the other room and then start with the talk of okay so i'm back in a couple of minutes i need to i have another assistant sorry okay okay professor rosa is in so christian so angelo so we can test we can test your screen sharing angelo so that uh we are sure there will be no problem afterwards you are muted can you see it yes doesn't work jovanni yes yes yes can i do stop sharing yes of course later it will not work professor busi yes i'll answer them right away as soon as people arrive because even before there are a lot of delays i will tell them in the breakout room okay perfect so at this point since adi i don't think that if i understood well angelo and adi will arrive later okay so maybe we can directly open the breakout room and do the projection test with christian micheletti okay i would have expected if there were some problems to defeat the participants but if it is automatic we can already open it i think no no i directly manually okay by hand they arrive okay i go please all join the breakout room oh here can you hear me you hear me now is that me or you hear me now is this is started can you hear me now okay yes so can you hear me now you hear me now okay sorry guys i was spoiled with my assets okay good perfect now uh i see you can hear most of you yes perfectly okay sorry for that okay um that's great so excuse me can you hear me yes i ctp i cts id services okay yes i can hear you so are you the host no no i got some host password in case but so because i think we are supposed to record just a second let me claim the host and promote you okay sorry just a second i apologize we have several activities at the same time and oh i really understand so just uh if i may ah okay i can claim host yes but you don't have the host key yes i do actually this you have it yes i have it okay try to do it by yourself and perhaps you received some instructions with the host key about recording to you actually not so that's just the problem so now i have i am host and i can't record but i just want to know what shall i do now so if you have to record then you'll have to put the files on a google drive uh to link share with you we will provide you uh this uh link and we will kind the ask you to upload their files and after this we'll provide upload them on youtube okay nobody wanted to have records will be uh record uh last setup where it's going to on locals on local computer please never record until later so you confirm me you confirm me that you did not receive any google drive share link it will be provided to you as soon as possible okay anyway you can hear me first question is quite simple does any one of you have chemistry before for me that's all it's totally new you yeah it's beautiful for most of you it's totally new you have physics that suppose of the atmosphere nothing is that correct i do a full adjustment because i see all the things that's not the i like it a little bit of like what's very curious i'm assuming that this is everything okay good so i did not you can register him we have to send the google drive and put it inside the file let me check the last thing you were saying sorry you know this uh covid is killing us so it's the last year we did all remotely so other questions it's like is it working is everybody happy okay so no there are two breakout rooms i don't know why okay let me do this i i'm gonna close all the rooms and chemistry okay now i guess everyone is in the main room not yet not yet there are still some people i think that there were two rooms by mistake it would be important to have a single breakout room otherwise we make gonna recreate the room and i'm gonna open it okay you should receive that alex your microphone is off okay great yeah i think the transition was very smooth now everyone is in the room so i think you can continue can you see my slides yes yes okay perfect and so i was saying that indeed what we want is that the computer made for us this task that it's to identify the groups in our data and we want to do it even if the data is in high dimensions and if the clusters our groups are odd shape we will see later what it means but before going there i want to say why clustering we are in a atomistic people works what i will not say event let's say and why we are talking about clusters let me show you three cases that are not all of them but maybe kind of general one case it's the analysis of a molecular simulation in this case our data it's it's games this is a protein so it's a convert sampling of this protein that has something like 10,000 100,000 coordinates and from this simulation what we usually want is to obtain the kind of information that it's in there right that it's exactly the conformers and to obtain the conformers can be done by clustering without with few knowledge of what's going on in the protein another test case it's the chemical chemical databases for instance i have four well this is four but usually it's millions of components databases and when i apply clustering i applied inside a pipeline that allows me to reduce the number of compounds that i want to test against a given target for instance in the case of jack databases another case that it's also has biological applications it's games when analyzing sequences this is a protein but it can be also applied to RNA DNA sequences where from just the sequences i can group them and and these groups can be useful for instance in the right i have shown an example for a from a paper in which they perform a clustering in protein sequences in such a way that they identify which clusters are more likely to have proteins that have a given property in this case where mood killers something like that i don't remember exactly but the idea is you cluster all the proteins and you have in the underlying hypothesis that similar proteins proteins that belong to the same cluster would have a high probability of having same properties and so when clustering i took this slide from my lessons in clustering you first start from data and then you usually perform some kind of feature transformation that allows your data to adapt better to your target and then you perform the clustering usually then you validate the clustering and interpret them and usually from this interpretation it's where the knowledge appears but this project it has some this pipeline has some feedback because when validating you can came back to perform a different clustering or even can make can make came back to a different feature transformation but let's start from the beginning for the data samples one thing that you have to have in mind it's how many objects are in my data set why one thing is the computational power let's say if you if you have millions billions of data points there are some kinds of analysis that you cannot afford instead if you have hundreds it's much easier but in the other hand one have to take into account that for some methods there is a kind of statistical sampling needed you can think about converts molecular dynamics you need many points for converter dynamic simulation so also that it's something that you have to take into account at the moment that you decide that your clustering method more important even it's how is your data described for instance in the case of the atomic coordinates that I put at the beginning your features are the atomic coordinates real numbers right in the case of the chemical library and your data your features are the structures some kind of descriptors but also the three destructors both 2d and three destructors in the case of sequences usually you just have the letters okay and once you have cleared this data you have to deal with the feature transformation and feature transformation usually implies three steps or may imply three steps one is feature selection one is dimensionality reduction and the other one is distance computing let's start for feature selection what I mean with feature selection well here I just explaining you what is that there are many automatic techniques but it goes far away from the purpose of this talk and the question is that for instance in the case of atomic coordinates I can wonder if all of them are irrelevant for my purpose if I'm interested in the folding of the of a protein probably I shouldn't include the water molecules maybe yes but probably not the same occurs with the side chains I mean for instance people working on folding again usually just include the main chain atoms but if you are interested in other kind of analysis probably you need to include the side chains or even you can be and you can need to introduce the water molecules Ali would explain as later why in the case of chemical databases and the question is that which descriptors are relevant for my problem and this is much more difficult to to get because and there is a lot of expertise for instance you can think about the log p measure of solubility the pharmacophore profile that it's a kind of 3d descriptor connectivity indexes that depends on the topology of your molecules and so on so far but there are so many that you usually need automatic tools for choosing them in the case of sequences what may happen is that in you have to clean somehow your sequences in order that avoid the introduction of not significant segments mostly let's say in in when you have monomers against dimers or something like that it's probably you just need to take into account some monomers regarding the dimensionality reduction it's a feel by itself I guess going to introduce some hints but I don't want to do the talking dimensionality reduction and dimensionality reduction it's okay independently of the data that I have I can try to reduce their features to few features in the in this case I have just two features and this reduction can be meaningful or not meaningful depending on the methods and on the system there are many methods that allows us to use to perform dimensionality reduction this scheme came from an already kind of old review from 2009 there are much more methods now aga days but well I would not explain them but just to say that it's an open still an open problem and why because it can be really easy or can be almost impossible in the case that you see in the screen you can see that this line it's kind of easily transformed in 1d and this can be done by principal component analysis that it's a technique based on the covariance methods and it's a technique that works in let's say in linear environments let's say in hyper planes however if you have something like this 3d point distribution you with pca you cannot reduce the dimensionality from 3 to 2 it will not work and it will not work because this surface is twisted and it's kind of topologically complex and however people have been working on that there are methods that work pretty well on non-linear projections but the question it can be even much more complex if you see these distributions and I say that it's just a 2d distribution of points but this distribution can be summarized in a line if you want but it's difficult it's one dimensionality but to put it in a single line it's topologically impossible okay so sometimes the projections have not are not easy to do and this can be seen in two cases for instance this is a simulation from the results from an all simulation that I made nine years ago and in this case pca works fantastically and projecting the coordinates of the backbone in 2d with pca allows us to identify two free energy minima that allows us to identify two conformers of this mini protein it's a peptide that falls okay instead in the case of biline head piece we try also to project with isomap the coordinates of this it's bigger protein it's 32 degrees and the question is that by projecting with isomap you can see that okay the ground truth it's the color code that tells us the degree of folding and you can see that the folded and unfolded points configurations are mixed and this happens because isomap it's not able to project in two dimensions all the complexities that have the configurations of the folding trajectory okay therefore in dimensionality reduction we try to project into the of three dimensions but okay if it works it's perfect you can almost finish there and if even if it doesn't work in two three d if you project in let's say eight dimensions probably it will simplify the analysis posteriori however if we don't do it properly we can have an important information loss and if the dataset lives in a complex manifold it's not easy it can be difficult or almost not even possible to perform meaningful projections the last point of feature transformation that I want to comment it's distance computing and the question is that most of the clustering methods relay in some kind of quantification of similarities the most it means that for clustering we need to quantify how similar or dissimilar are two points okay two data points in the case of proteins would be configurations in the case of the chemical database would be compounds in the case of sequences would be sequence okay dissimilarities for thinking about clustering can be interpreted as distances and that's important because it allows us to reasoning in clustering terms and the question is that the lower the distance the more similar are two points that are in top of the order would be identical two points that are really far away would be really really different but our definition of distance depends also on the data type that we are dealing with there are some general distances that are pretty used like minkowski distance that it's a generalization of the Euclidean distance you can see that with d equal to i with p equal to two this recovers the Euclidean distance or the cosine distance that just take into account the angle between the vectors describing our data there are distances that are defined for molecular systems like the rmsd or the diagonal distance that defines its the Euclidean distance taking into account the periodicities of the dangerous angles also for binary molecular descriptors we have the jacar distance we have this hamming distance that allows us to compare two protein sequences once they are aligned the hamming distance it's increased by one if the amino acids are not the same or set to zero if they are the same so there are many many distances I just put here some of the most used in our field and finally we can start talking about clustering real clustering okay as I told you before well the clustering is relatively easy for humans but not always it's easy I mean now I'm going to show you many clusters obtained from this distribution of points what would be this that it's kind of trivial but you can argue that all of them could be correct so at the end the clustering result depends a lot in our definition of what is a cluster and of course we have to define a cluster according with our target when we perform clustering and this is the reason one of the reasons for which there are so many clustering methods okay however they can be somehow summarizing three types one is flat clustering that it's it performs just a hard partition of the data it's what we have all in mind when we talk about clusters it's just a sign it's data point to a group and I put here some widely used methods for perform this flat clustering and fancy clustering it's a bit more complex because the assignment to a group it's not univocal but it's a you give to each point a degree of membership to its cluster here there are other methods that employ fancy clustering and finally there is hierarchical clustering that generates a tree instead of a single partition and this tree it's you can see a kind of hierarchy I mean for people that have seen let's say nature programs where let's say the families in the animals or the taxonomies taxonomies are kind of hierarchical clustering okay let's see what are these points let's say in flat clustering everything it's easy let's say I have this partition where points in red belong to cluster one points in yellow belongs to cluster two points in green to cluster three and so on in fancy clustering I have a kind of palette of colors right I would say that cluster that this point the point that I'm signing with the arrow has a 90 percent of degree to cluster one nine percent of degree of membership to the cluster two and a very very few degrees of membership to other clusters this other point it's almost in the half between these two clusters so it has a degree of membership to each of them and also to the third one this one it's kind in the middle of many and so on so far okay hierarchy clustering makes something more complicated but by generating a kind of hierarchy you can recover the clustering instructor okay but this clustering instructor it's difficult it may be not easy to transform in flat clustering for instance in this case the two clusters are easily recovered but for recovering the five clusters I have to do a kind of strange cut right however there are some uh there are other differences in our clustering for instance instead of inside the flat clustering category I would like to remark two clustering methods I would say the partition methods that allows you to put together points that are similar my density based methods allows you to follow the profile the density the priority profile of the points distributed in the in your data the difference is that I mean there is not a correct clustering it depends on what what is the utility that you are going to use this clustering for according to your target you may want to use a partition method or a density based method okay for instance a typical case of k-means clustering of partition methods it's k-means clustering it's probably the most used clustering method employed and it works pretty easy let me explain you quite literally the first thing that you do for instance in this dataset is to randomly pick case centers you have to decide how many clusters work in this method you randomly pick them and then you assign each point in your data to its nearest center once you have this clustering partition you can recompute the centers that somehow will move okay and then you can iterate and by iterating the clusters I mean somehow you find an optimal and the linear partition of your data the only thing is that this method depends of course in the initialization in this case you can see that for this initialization there are two clusters that are divided by two while there are two clusters that are merged due to the fact that my initialization was not perfect okay different method it's based on density on density I would want to explain you its density peaks clustering and in this case like in all density based clustering the first thing that you have to do is to compute the density for each point and the density it's nothing else that a quantification of the number of points in the neighborhood of a given data point once you have compute the density that it's kind of trivial compute you compute the distance from the nearest point with higher density and we call it delta and then you plot this delta as function of density and what happens is that the points that are outliers in this graph happen to be centers of putative clusters by picking these centers once you have picked them you can try to assign its point for instance this red point by following the profiling density and arriving to a given center once you arrive to a given center to you assign all these points to the same cluster sorry therefore if you do it for all the points you finish having a full partition okay okay I don't want to explain you much more methods of clustering also because I don't know how much time I have Giovanni yeah a couple of minutes okay so I just want to finish with some applications and I can okay let's back to the applications that I told you before imagine that you want to cluster the billing headpiece by using a mix of density methods with hierarchical clustering you can obtain something like that that translates in this free energy profile okay this free energy profile you can obtain it because you have the densities by using that then feeding a Markov state model with this output you obtain a five states Markov model for billing headpiece okay another application it's in the field of chemical diversity let's say these people just make a hierarchical clustering based on the scriptors of the compounds mixed with the fungal they are fungal they came from mushrooms mixed with the genetic analysis of the of the mushrooms and they managed to obtain this nice hierarchy that explains how the diversity on these products was worn finally in the case of protein families we work in with the pure family and we obtain that this clan that it's a clan the clan of poor can be divide in many families according to the the clustering results are in the left while the ground truth is in the down and you see that even not exactly somehow the clusters let me show it let's say all this part of the dendrogram that comes from the cluster reproduces this family this part of the dendrogram reproduces this family almost perfect and so on so far let's say the color code it's the purity of a given cluster in architectures coming from these families so just having shown that clustering can be employed for many things in our field I just want to thank you and I will be happy to replay any questions okay thank you Alex so now and thank you also for being in time so now we have time for questions okay so there are questions on the chat I will read them so one question is can be hierarchical clustering associated with decision tree in machine learning uh no I would say it's a different thing I mean decision trees are based on single features let's say but while in which for each feature you have you take a decision okay let's say if a feature is bigger than a threshold you are in a in a class if it's lower than the other threshold you are in another class while here the hierarchical clustering it's dealing with the all the features at the same time it's taking us in the distance so it's a bit different so there was uh Uriel asked raising the hand but I cannot see anymore so let me see on the chat so Isabel Luisa wanted to ask a question so yes go ahead thank you for the interesting talk I was wondering about the feature selection for example if we want to check the peptide confirmation from a trajectory is it useful to use many features like RMST hydrogen bonding and also dihedral angles or is it better to stick to one well what we do usually it's to use many of them and then compare the results of the procedure okay if your features I mean if according with our feeling it's that the all the these features should give you comparable results otherwise you are having some problems yeah so this is a kind of sanity check for our methods we're taking many different metrics and we see they are giving you the same result okay that makes sense thanks okay then we have a question from Daniel who is also raising his hand I will read the question then Daniel just stop me if I don't read it correctly why the center points happens to be the outliers I think it's referred to density peak class okay the idea is that the key point is the delta definition in which you find the minimal distance to a point with high gas density okay so the question is that the maximum even points with high density have low the low delta if they are near another maximum right so at the end you are finding maxima in the density distribution I don't know if it's clear yeah yeah thank you thank you Alex. Then a question from Andrea can you explain how to perform a validation for clustering? Yes but it's a bit long the question is that I decide not to include it first well mostly they are okay let me short make a short introduction to that there are two kinds of validations that you can perform there are internal validations that depend on the structure of your clustering and external validation in external validations you are comparing with a ground truth and you have metrics like normalized mutual information for instance for comparing with ground truth in internal validations you check some characteristics of your clusters but the problem with this internal validation is that um till the moment they heavily depend on what do you think your clusters should be which not it's not always the case so the problem is that many cases when you compare internal validations in cases where you have a ground truth it doesn't happen that the best clustering is the one with the better internal validation index this is a bit delicate okay then there is a there are two questions from Suman the first is how to find or choose an optical metric to classify a given set of data because the efficiency of clustering the data by this matrix can defend can depend on various factors and the second question is how to pick an optimal machine learning technique like support vector machine or macro state model to explore a particular problem should it depend on the complexity of the system okay well for the first question I would tell you my experience is that the best feature selection is done by humans and let's say human experts are the better ones in choosing features and then once you have these features you adapt your metric to these features however there are many let's say many techniques that allows you to automatically choose some features all of them are relayed somehow in a kind of ground truth so what you do usually it's trying to reproduce a ground truth that not necessarily it's in your system but maybe in a similar system with some features and then you just pick the features that better reproduce these ground truths once you have that you can assume that in your system will happen the same and take the same features then of course the distance will depend on these features okay then the second question was how to pick an optimal machine learning technique to explore particular problem it's very general question but that's a really really general question I mean I also because there is not one method