 Hi, I don't know if you can see me. Yes. Great. So, let me share. Can I, am I allowed already to share the screen? Yes. I should go to, on top of Zoom, there is sharing. Let me see. Okay. Good. All right. So you can see my presentation. Yes. Perfect. Okay. Good. Okay. Great. I'm very happy to be here. And that also this year we manage anywhere and other to do this, this school, which is for us extremely important. As all of you know, there will be time also this afternoon. We have a gather town session where you will be allowed to ask a question. Well, to the speakers, I will be there for sure. After two 15. All right. So, so my top today is dedicated to an introduction to a very, very important topic in molecular simulations. It's a, okay. I would like to keep it very informal. So if you want to interrupt me with questions or curiosity, I'm more than happy. Otherwise, you're also welcome, of course, to, to ask in the gather town session. All right. So molecular simulations are extremely useful. And they will become even more useful. One of the reasons why they are so important is because it is well believed that they will be the key for understanding how proteins are working. So let's say that this is our, our, let's say, ideal goal that we want to address. Of course, there are many other important goal that one can address with molecular simulations, but through my, across my talk, I will mainly focus on protein and how they work. So the, let's say the work horse that one uses to simulate proteins, for example, is molecular dynamics. And molecular dynamics basically, basically implies solving the Newton's equations of motion. These ones, this is the mass of the particles, the positions of the particle is the second derivative. And here I have basically the gradient of a potential energy function. So modern molecular dynamic codes are extremely efficient are parallel and highly scalable. In order to arrive at this point, it wasn't well necessary invest work. Well, here I wrote three decades. I should actually say almost five by really, really many, many people here. The, the, the number of counter emotional, which were absolutely crucial to make molecular dynamic code faster efficient is becoming uncountable nowadays. So here, but still when, so there's, we are going to discuss during my talk, the efficiency of, of these codes, which are now a days available are still really not sufficient to do brute force simulation. So here I see a questions. Okay, no. Okay. Well, maybe if you have a question is better if you simply unmute yourself and do it directly in the microphone. Okay. So, so basically, there are, in order to perform simulation over a realistic system, for example, these membrane channel that we see here, one has to address to cope with three competing demands. So in a way one would like to simulate systems which are large. Since history and interesting systems are large and in homogeneous like in this case, I have the channel, then I have the, well, the molecule that is trying to pass across this channel, then I have the membrane, and then I have the water molecules. Moreover, I have a typically a problem with time scale as we are going to see. And finally, we have a problem with the accuracy. Somehow the more accurate the description of your system is the more computationally expands expensive. It is. Okay, so let's start from this last point, accuracy, which level of description should one choose. So you're, so let's say there are even cheaper option, but let's say what for us, it's typically considered the cheap option is describing your system with a classical potential. So in a classical potential, the molecule, your bio molecule, for example, your protein is described basically as a set of charged spheres, which represent the atoms linked by springs, which represent the bonds. Okay, so I have no quantum effects on atomic motion. So our atoms are purely classical. No electrons, no chemistry. So therefore here it means that I will not not be able to break this bond or this bond or observe any, any subtle effect due to the pH, like the ones that we were mentioning in the previous talk. So the force field is a potential energy function and the set of parameters entering its definition. So this is what we call a force field. So it is designed to reproduce basically the geometry of the molecule and some selected property of the molecule. So for example, here, this is the side chain of an amino acids in particular tryptophan and the force field will be tuned to reproduce, for example, the salvation free energy of a tryptophan or the lipophilicity and well, in principle, many others. So this is where the enormous amount of work from many generations of researcher is actually so this work is written in the parameters of this force field. Okay. So this is how it looks our potential energy function. It looks complicated, but finally is just a complicated function of the coordinates. Okay. So here this, as I said, this approach, which is based on classical force field is what we call the chip option. So the accurate option implies dealing with the electrons. So during this week, we will hear about the applications in which it is necessary dealing with the electron. So like for example, if you have an enzymatic reaction, you must deal with the electrons because an enzymatic reaction involves a chemical reaction and a classical force field is really not able to describe a chemical reaction in any manner. So if you want to deal with the electrons, you have to basically solve the Schrodinger equation. And then after you have solved the Schrodinger equation for a given configuration, then you must evolve your atoms using the forces which have been derived thanks to the solution of the Schrodinger equation. So the manner of doing that, so you must in a way solve at the same time the Schrodinger equation for the electrons and the Newton equation for the ions. So the manner of doing that was actually developed here in CISA, well, almost 30 years ago by Carr and Parinello. Okay, so the enormous advantage of this approach is that, well, there are no free parameters. So here, if we go back to these lights here, these functional forming includes a lot of free parameters like the force constants of the bonds, like the charges of the atoms, the Lennard-Jones parameters. Here if you do it in this manner, all of these things, well, in a way the only three parameters at least in principle are, yeah, well, just the charge. So there are basically in principle no free parameters. Let's put, make things simple at this level. But of course you pay an enormous price. So this enormous price is that this approach is way more expensive because basically at every configuration of your system you must solve the Schrodinger equation. Okay, so here, simulation of realistic system, what can we afford? So here, well, for example, let's say that we want to simulate the HIV protease using classical potentials. Here, since I don't have so much time, I will simply go to the final result. So basically, basically in, so if I want to simulate this system on my personal computer, basically I will be able to simulate one nanosecond of dynamics in one day. So I will be able to basically see how the system evolves in one day for one nanosecond. So one nanosecond sounds like a very, very short time, but actually this implies computing the forces on your system for half a million times. So this is something which of course decades ago would have been science fiction. Nowadays you can do this on a desktop computer which everybody has in the office. Okay, so this is, so well, basically, so if we are using a classical potentials or no chemical reaction, nowadays you can simulate one nanosecond on a desktop computer for a system with 50,000 atoms. Now, if instead you want to use a quantum potential in which you are able to describe and treat a chemical reaction, well, basically you lose two orders of magnitudes in achievable simulation time, but even more importantly, as you can see, you lose basically, well, almost three orders, let's say two orders of magnitudes in system size. So while with the classical potential you are able to treat basically routinely 100,000 atoms in a quantum potential so doing carparinelomolecrodynamics, basically you can treat only systems only with 100 atoms. So this actually means that it is practically impossible with ordinary computational resources to simulate a full protein in water solution with a quantum description. Of course, if you are using a supercomputer, this is now possible, but not with ordinary resources. Okay, so here this is something which I'm going to skip. So now we immediately see that these simulation times and these sizes which are affordable with ordinary resources pose an important problem because, okay, let's stick to classical molecular dynamics. So let's say that I am able to simulate with important resources that we have, for example, here in CISA, 10 to the minus five seconds per month. So if you are using a dedicated, very large supercomputer, you will be able to simulate one millisecond in one month. But on the other hand, protein folding, which is for example something we are very much interested in order to occur. So this requires simulating like something between 10 to the minus five seconds for very, very fast folders to 10 to the one second. So 10 seconds for very large proteins. Face transitions like face transitions in solid state physics, for example, this is a face transition in a zeolite which we are going to see in a second. Well, actually take place on time scale which can be really, really extremely long. Let's say of the order of physical hours. So this means that these simulation times that are affordable with ordinary computational resources are just not enough for simulating this process. So a big issue is even worse because in principle, if I have a very large supercomputer, I will be able to simulate one microsecond, microsecond of dynamics in one month. But chemical reaction are typically much slower. So like for example, if I am in a lab and I mix reactants in my pipet, then the chemical reaction can take once again an hour or a day to occur. So how am I actually able to use molecular simulations to derive something meaningful and something useful with the relatively short simulation time that I can afford, let's say 10 to the minus three seconds for classical MD and 10 to the minus six seconds with a big issue. How can I use this short simulation time to derive information about something which occurs on a much longer physical time. So here, how is this thing possible? So here, let's try to see some examples. So here, this is the folding simulation which has been generated with an un-sampling technique which I'm going to focus on in a while of a folding process which occurs in 0.1 seconds. So here, let's look at it again. So even if this is a very, very complicated process, still, and which normally occurs in 0.1 seconds, it is possible to observe this process using very moderate computational resources. So basically only a desktop. So here is a second example. This is a phase transition of a zeolite. So this is also a process which would take place in minutes in a real life experiments. Still, even if this would take minutes in a real life experiments, so it was possible to simulate these transitions using ab initio molecular dynamics. So here, this thing is a dynamics in which the electrons are treated explicitly. And this was possible to do that 10 years ago. So how is this thing possible? Even if I told you that it's possible to simulate only these processes, well, in principle, one should be able to simulate minutes of dynamics of the system. But in practice, I can simulate only 1 nanosecond. How is it possible that I am able to simulate only one nanosecond, but I am able to observe events which occur on the scale of minutes? So the goal of the rest of my talk will be to give you a hint on how is this thing possible. So, and this is actually where we actually go to the focus of my talk. I want to give you actually a hint on how and why, how can one enhance the occurring of rare events with targeted techniques. Let me see what time it is, yes. All right. So here basically, as I told you, it's possible by 10 to the minus 8 seconds of simulation to get information on processes which occur on, for example, 10 to the minus 1 seconds. How is it possible? Let's give a close look to the system. So they think that one normally has to do in order to, well, implement, let's call it this miracle if you want to call it like that, is first of all, one has to find a function of the coordinates which is likely to take very different values in the different states. So this function will be called s of x. So for example, here, well, here in the example of the zeolite transition, it will be, this function will be the box shape in a chemical reaction which is another example which I will give you. It will be the bonding pattern. As you can see here, this is azulin and this is naphthalene. As you can see, the bonding pattern is totally different. And here, if I want to study protein folding, for example, I can take the fraction of alpha edicts which is very different in the unfolded state or just the number of contacts. So after I have found this function of the coordinates which takes very different values in the different states of my system, then, well, what I can start wondering is how would s of x behave as a function of time? How would it behave? It would behave actually like that. So this is time. This is, for example, let's say my fraction of alpha edicts in my protein. Here, well, here it's, this is, let's say, a little bit arbitrary, the units on this y axis. But basically, basically, here I have that I have a transition between a state in which the fraction of alpha edicts is small to a state in which the fraction of alpha edicts is large. Here, basically, the time before the reaction, before the folding event is basically this one. As you can see, this fraction of alpha edicts is simply oscillating up and down. Nothing happens. Here and then, all of a sudden, I have my folding event. And this folding event is actually extremely short. Here, you see that here I have oscillation in, let's say, the unfolded state. And then, all of a sudden, a folding transition, and then my system folds. So here, in a molecular dynamic simulation of a chemical reaction of a phase transition and so on and so forth, actually, the system spins most of the time oscillating in a local minimum, maybe the folded state or the initial phase where I start my simulation. Only very rarely, the system performs a jump to another state. The time required to perform the reaction is actually typically extremely short. So now, the key trick, which is at the basis of all the non-sampling methods, which one can basically imagine, is finding a manner to simulate only the jump. So here, in this case, instead of wasting my simulation time to simulate all this phase here, which is the time before the reaction, I basically concentrate only on this jump. So this jump is extremely short. The time required to perform the jump is extremely short. Therefore, I will be basically able to gain a lot of computational efficiency. So now, the thing is how to do that. So this is where the different method be fair. So I can basically, yeah, well, for example, some methods for enhancing the sampling require pulling the collective variable S. So it's like, for example, if my collective variable is the fraction of alpha elix, I can put a spring in my molecular dynamic simulation, which basically forces the fraction of alpha elix to become larger and larger. So this is what, let's say, what you do in Steer molecular dynamics and also in a method which is called thermodynamic integration. So another class of approaches is a little bit more advanced, let's say, and in a way, it implies making important sampling on reactive trajectories. Basically, the folding simulation of that I have shown you before of this protein with a knot, in a way, is done by a method which allows basically selecting a priori only trajectories which are reactive, where in this case reactive means trajectories which are associated with the folding event. Another class of method, which is the one on which I'm going to dedicate the last five minutes of my presentation, are methods in which you basically flatten the free energy. And now we are going to see what this thing means. So here, the name of this method, which actually attempt flattening the free energies are, well, umbrella sampling, metadynamics, adaptive force bias, and Wang and Landau sampling. So as you can see, there are many, many different methods. They are clearly in a very short presentation, like the one that you are seeing today. I will not have time to really go into any detail on each of these. I will only give you a glimpse, an idea of what you can do in a specific case, in this one. Here there is yet another class of method, which implies rising the temperature of the collective variable or of the soil. A lot of things. So here, how do you flatten the free energy? So here, let's start from this, so this graph which I have already shown you where you have basically the value of the collective variable as a function of time. So here from this trajectory, you can compute the probability density, which is basically the histogram of this collective variable here. And here, if you compute this probability density, I will have two peaks, one here corresponding to this state here and another one there corresponding to this other state here. Okay, so here from this probability density, if I simply take basically the logarithm of the histogram and I basically multiply it by minus KBT, you get what we call the free energy. So the free energy of this specific state will correspond like this. To this here, I will have two minima. This minimum will correspond to this probability peak. This minimum correspond to this other probability peak. So here in a free energy landscape, I have basically as many minima as states. Here I have two states, here I have two free energy minima, one and two. So these two free energy minima are separated by a barrier. The highest the barrier, the more it is difficult to go from this minimum to this one. So if I have a very high barrier, basically I will never be able to observe a transition. Okay? So here, so the general idea of these approaches for simulating rare events, in which you flatten the free energies, really trying to go from this free energy, which looks like that to something where the free energy is flat. I basically get rid of my barrier. How do I do that? So basically the classical manner of doing that is by using a technique which is called umbrella sampling, which was basically born together with computer simulations. It was born in the 60s because this problem of having like metastability is not something that was invented recently. It's something that existed where basically people started doing molecular simulation and realized that this was a problem basically immediately. So what do you actually do? So you add an external bias. Let's say that here I add an external bias, which has this form here, the sum of two gaussians, one localized here and one localized there. You can see how this bias looks like. So basically the sum of my free energy plus this bias will be this red line here. Now if you do your simulation under the combined action of your potential energy function and this external bias, then you will generate a trajectory which will look like that. So as you can see now in this case, here in this case, I will observe only two transitions event in my simulation time. Here in this case, I will observe many transition event in my simulation times. So here too, here, like let's say 100. So basically by adding this external bias, I am basically doing what I told you that was the key of all the nonsampling methods. So namely using all the available simulation time to observe transition events. Okay, so here the thing is, so if you basically, so here the reason why in this specific example, adding this external bias works so great. So it's because basically I have sort of invented a functional form for this external bias. So here I have invented that it is very good to use as an external bias the sum of two Gaussians, one localized in minus 1.05 and of height nine and another localized in one with height five. But how do you actually know in advance how to choose this external bias? So this is highly nontrivial because clearly it's possible to write this form of this external bias if you know how the free energy looks like. So there are many methods on the market which allow you to reconstruct automatically an external bias with the correct properties in a sort of an automatic manner. One of these methods is called metadynamics. So in metadynamics you basically well choose a collective variable S of X and then you bias the dynamics with potential which is basically defined in this manner in which instead of putting only two Gaussians you put an infinite number of Gaussians very large number of Gaussians basically you put a Gaussian every step of dynamics which you make. So here, so these external bias which you make sort of iteratively compensates the underlying free energy and the sum of your underlying free energy which in this specific example looks like that so you have basically two minima plus your Gaussian becomes iteratively flat. So the manner in which this thing works exactly is well in order to explain it to you more regularly I would need more time but if you are curious of course I will be available in Gallertown this afternoon. So here this is an example of a difference of what happens if you try to simulate a chemical reaction which is a nasolint to naphthalene transition with ordinary molecular dynamics in which you remain trapped in a local minimum and you simulate it with metadynamics. So if you are trapped in a local minimum your simulation goes on basically oscillating back and forth in the same minimum you have no reaction while here you see that due to the fact that I am iteratively filling my free energy landscape I am basically forcing my system basically to move from one minimum to the next so here this is of course only a pictorial representation here in this case in this chemical reaction I have something of the order of if I remember correctly six different free energy minima and I am basically forcing my system to move from one minimum to the next by adding these gaussians and so as you have seen here in this case I have managed to perform a full transition from azulin to naphthalene by adding these gaussians iteratively in my system. Okay so clearly here well so this example which I have shown you is of course only a toy example the same approach can be used to simulate much more interesting systems like for example one can simulate the nucleation of an amyloid here I don't have time to go into detail but clearly if your system becomes complicated like for example the nucleation of an amyloid you have to choose complicated collective variables so here in this case you have to choose eight different collective variables the number of hydrogen bonds the number of hydrophobic contacts and so on and so forth and then basically you end up with the free energy landscapes which are intrinsically multidimensional so in this case I have the minimum number of dimensions in which you can meaningfully visualize this free energy landscape is three these are the three collective variables described in this multidimensional landscape you have the lateral anti-parallel beta bridges so other three variables it doesn't matter how they look like but basically then I have three states here I have the disordered state then I have a quasi-ordered state and then I have a non-trivial transition to something which is really the fibril which is actually hidden here here I have a state which is ordered but it's not fibril and in order to go to the fibril I have to cross this small bottleneck up here here well here then you can apply this also to protein folding also in this case I need many collective variables and the landscape well typically is highly non-trivial and strongly multidimensional here basically all my research work in the last year has been really devoted to find a manner for example to find the correct collective variables which is highly non-trivial and also to visualize and to understand how multidimensional free energy landscape looks like so here these are actually open problems how one can find automatically the best collective variables and moreover how can one visualize and understand the free energy landscape in which you have many transition complex conformational landscape how is it possible to analyze this thing automatically so in order to well to basically solve these problems well the tools that our community starting to use are more and more stolen or let's say hired from data science and machine learning so in the next days you will hear some specific talks which are basically devoted to well exactly this thing so how you can use data science and machine learning for example to find well the best collective variables or to understand how a multidimensional free energy landscape looks like okay so with this so my presentation is finished I think there is still a little bit of time for a few questions so I don't know you can either write the questions on the chat or simply unmute your microphone and ask it directly hello can you hear me yes thanks for the talk I was wondering in the case of a nucleation processes that are highly cooperative like the one you just showed can you try to turn off the bias once the process has started and you know and let it run naturally without the bias indeed you should in the sense that especially for complex processes after you have sort of understood how the process is happening qualitatively and this you can do it for example using meta dynamics then it is very very well very useful to revert to other approaches like transition path sampling where you basically do exactly what you said basically after you have found the transition state you basically launch unbiased molecular dynamics simulations from your transition states and you see how the system would have evolved spontaneously so this will actually give you the final let's say unbiased picture of how the transition occurs but it should never come on their own it doesn't exist a method which you can use on its own you always should use these methods together so for example in a for study nucleation for example you can first use for example meta dynamics or umbrella sampling and then after you have a preliminary picture of how the transition of course you use for example transition path sampling indeed so then I see maybe a question on the chat you suggest that the rising temperature could also fasten the calculation wouldn't it affect the stability of the system is the temperature is rising indeed the answer is absolutely yes you are totally right therefore you don't well basically there are techniques which allow you to basically reweight your results reweight your results means that let's say that for example you use an approach in which you rise the temperature only of your collective variable let's say that you put your fraction of alpha elix at 600 Kelvin while you keep everything else at 300 Kelvin no so then clearly then you change your ensemble of in which you are treating your system but there are techniques which allow you to compute how your free energy would be you would have performed your simulation at 300 Kelvin so these are called reweighting techniques so these are techniques which are based on statistical mechanics are techniques which are regroups are exact so they are based on to therefore it is possible even if you simulate yours you basically keep one collective variable at high temperature to then estimate your probability density at 300 Kelvin so here so this your question is highly appropriate you cannot simply blindly rise the temperature you have after your performance simulation at high temperature you have then to reweight your results unfortunately here I have to be a little bit qualitative because in order to explain you how all of these things are working I would actually need the well 40 hours which is basically the duration of a typical course on this stuff so I'm sorry if I am a little bit qualitative you have my sound Alessandro yes thank you for your presentation I wanted to know that what is the difference between using reactive force fields and these methods you talked about in studying a reaction or transition state well the problem is that reactive force fields have to be parameterized and parameterizing reactive force field is an open challenge in the sense that of course there are reactive force fields which work for some specific reaction but if I take a generic reaction let's say a reaction involving for example a metal organic complex which nobody has seen before and therefore it's interesting scientifically interesting there either you spend a lot of time parameterizing your reactive force field or the only way to go is using quantum mechanics so there are approaches which allow you to do like for example QMM which allow you to treat with quantum mechanics only your reactive site and the rest classically so this is possibly the simplest way to go so well here to wrap up the answer to your question reactive force field are in principle great but they have to be parameterized and therefore they are not available for anything that you might think of alright so maybe since we are a little bit I think we should now it's time for everybody to take a break I think we can actually close here as I said I will be available to answer to more questions also well I can try to be a little bit more specific if necessary I will be available in gatter town this afternoon after 220 because I have to I have a meeting at 2 but starting from 215 to 20 I will be available alright so I think we can directly see there so for the mean in the meanwhile I wish you a great lunch