 So, after two days of the school, we got familiar with high-performance computing in general, different polarization techniques, and yesterday you learned how to efficiently max for molecular dynamic simulations, one of the very powerful methods for studying of molecular systems. And today we are continuing to cover two additional areas that are extensively used in molecular research. These are free energy calculations and docking. So free energy calculations, you might be familiar, is a powerful method, for example, for scoring drug candidates, and in combination also with docking, they give very powerful tools to researchers. So first, this morning, we will discuss free energy calculations in use, automatically, efficiently. For example, Gromax is a backend by using the PMX application that you will learn about. So, it's my pleasure to introduce you to Vitatus Gapsis, who is the main developer of PMX. He will tell you more about the method in general and also the tool itself. And I will find it very useful in your search work. So, Vitas, the floor is yours. Thank you for the introduction, Rassan. And let me share my screen so we can start right away. Now you should see my screen. Let me know if there's something wrong. But yeah, let me then begin the introduction in what we'll cover today overall. So I decided that it would be probably a good start with more broader and more general introduction to the free energies, what kind of methods we have to play free energies from the data and why in general, why they are of interest. So Rassan already remain in applications, but we can also go a little bit into the details why in what particular questions free energies might be useful to calculate. And then in this would be my first part of the talk. And later I would show you in the next main application. So applications we encounter in our everyday work. So I work together with Bert de Groot in the computational biomolecular dynamics group in Max Planck Institute. There we only do computational research and we always ask questions about protein thermostabilities. We ask questions in ligand binding and several examples I'll show you today. And then after the talk, we have also practical hands-on session. So there I would go even further into the details. And then we really can have a look how to set up such calculations and how they can really this BMX and Gromach's combination can do some useful things for you. All right. So let me start right away. So free energy calculations, first, firstly, let's go to basic question. Why care about free energies? Where do we find these questions related to free energies? So the feature that already were mentioned by Rassan, those are affinities. So for example, imagine ligand and protein. So a common question in the drug design field, how strongly does the ligand bind? The binding itself is synonymous to the free energy difference. So if we are able to calculate free energy difference, we actually also already have access to the affinity. In other words, we know how strongly the ligand interacts with the protein. Really for protein-protein binding, it's exactly the same way of, also, stability are free energies. Consider a protein folding example. Protein may prefer to be in its unfolded. So if we tilt the free energy into the direction of the folding state, we then make the protein more thermally stable. This principle, again, is just a matter of calculating energy difference between the unfolded state. Also rates, we often consider rates as a kinetic parameter. But if you express that, yeah, as a relation, rate is a relation to the, has direct relation to the free energy barrier between the potential of mean force, for example, of how iron crosses a channel or water molecule across aquaporin channel, aquaporin protein. It also crosses on some certain geolandscape. And the barrier, then the crossing will be, then the channel will be less conductive. If there is a lower barrier, then it will be more conductive to assess the free energy landscape of this transition. So I hope I convinced that free energy calculations are very many, many different locations. And what methods, what flavors do we have for the free energy calculations? So yeah, this is a very rough sketch. So I don't need to do some attempt at a really fine grained division of the methods. Just my rough interpretation. So let's start from the right side. Those are statistical methods that I separate there in the separate branch. Statistical meaning that we are not using physical principles, or even if we are using them, we are approximating them CV. Those could be ligand based and structure based. So imagine ligand based statistical methods are the ones where we ask if we have now a bunch of ligands, we don't know anything about what they bind to, what they interact to. We simply try to establish a regression between some descriptors, maybe there are a number of atoms, number of hydrogen bonds that the ligand has, number of rotatable bonds and free energy. So these would be very chemo informatics based approaches. Structure based approaches would already take into consider the protein ligand interface and would perform docking into these binding pockets. Hybrid methods, they combine both physical, physics based, for example, sampling approaches as would be Poisson ball and accessible surface. And then regression based on these samples, once it is constructed regression, approximate the free energy differences. Or statistical force field could be used as Rosetta or Foldex, for example, used. They use statistical force fields, but the local sampling in that force field and this already brings them into some hybrid between statistical and first principles based. And first principles based methods, those are the methods that we'll be using today or discussing today and using later. So this is the whole zoos expended there more and those could be free sampling, bias sampling. Then we go into alchemical methods, enhanced sampling, and we will discuss further into those. So let's go branch. So before we just jump in, before we into them methods, how to extract free energy from the calculation. Let's recall a few ways to express free energy. So the first relation, let's have some of the first relation, you probably know it very well, it just relates enthalpy and entropy and the enthalpy minus would be weighted by the temperature free energy. So this is a thermodynamic description of the free energy and another lesson, let's have a look at the how from this point of view, we can express the relate free energy of a state I, we can relate the probability of an article or a system being in that microstate I. And now we'll go over approaches that will utilize, give us insight into these both into both of these relations and we'll express the free energy or extract the free energy difference from the, so let's have a look at the first example and this very simple example, but it already captures or in the mainly intuitive nature of these relations that I just showed. So imagine we have a peptide, which is able to unfold, and we simply monitor the RMSD from the from some reference state, and in the top, we are running at 298 Kelvin at the room temperature we're running it, and we mainly remain below the red light state, sometimes we transition into the unfolded state but very rarely. Now, in the lower panel simulation. Now we are running, sometimes we're still in the folded state, but now almost let's say. percent of the. Higher into the unfolded state, so we keep on unfolding much more often are certain edges. And now the these these these two panels already illustrate very nicely how we can extract the free energy differences, so remember that the three are. Well, they are nothing else, but the probability probabilities probabilities of being in one state, but we simply can count frequency of occurrence of a system in unfolded state versus the folder state and use this relation that I showed. So this kind of definition ratio of the probabilities will come out to relate to the delta G between the two states and we need to look and extract the delta G counting the problem or frequencies and based on the law of large numbers we just relate them to probabilities. Okay, and another feature, we see the effect of the temperature, we change the temperature we change we shift it also the free energy balance to the more to than folder state and we can go back against the happened, so we had our. We all of a sudden increased the entropy contribution, because we just changed the tea to a higher. The gene this case it would be delta G because we consider the two states the difference between the two states we shifted it to another. So you can go even further, so this was just in RMSD space, we can also expand it into the a little bit more into the conformational space density and notice that they were not just folded and folded there were several folded states so that this is just a principle dimensionality that. reduced dimensionality every point now represents a different confirmation of the peptide. And we notice that the basis of different different conformations and all the rest is there unfolded let's call that unfolded, can we extract the free energy differences between those. When let's continue on simply let's count how many points are in each of those, and we can again just let's put the, this is a multi three dimensional. Some coordinate, and we can see those three basins populated nicely, the first one is the deepest, and it has the lowest, the most occupied by that, then there will be the second and the third. And now, if we look at it also, color by the temperature, by which, at which this perform, you can see already that this very nice energy landscape changes substantially the temperature, all of a sudden, where barriers are no longer barriers. The, you could consider it to be much, much, much flatter this. Yeah, so this very simple example already shows us all the particular features of how we energy is an edit sense and how we can control the transitions between barriers, just by changing the temperature. But, say, sometimes will, yeah, we know that using temperature as a trick, we can overcome the transition barriers, we can, therefore, you start constructing some replica chip based replica exchange schemes, and so on. But let's, let's say we are interested at a free energy landscape at a given given temperature. We are faced with a situation where we're where our particle simply can sample just one side of the barrier, the barrier, this barrier, it's, it's quite high and we never cross it so we never observe a transition, but we're interested in learning is the landscape is the free energy landscape and what is the difference between the free energy values on one side of the barrier and on the other. How is this so as time would be umbrella sampling and with an umbrella sampling. And I mean, placing an umbrella potential so what practice, we take this particle, let's, let's imagine now that this particle is actually water molecule. We restrain with a potential at a given position and allow it to sample, sample the landscape as as wishes. And if, if we are, let's say in a completely flat landscape there is no, yeah, no gradient in any direction it will simply sample this ocean as defined by potential. But if there is, if it is on a, yeah, some current free energy landscape, it will slightly tilted. It will have a sample, a little bit preferred direction. Later, we shift them a little bit and do the same. Now, the blue molecule would be in the place of one red molecule. Then we do the same, the same, the same sample across the reaction coordinate. All right. Now, we have sampled them again. As it wishes to sample, we only need to unbiased the and we in principle rely again on our counting. Just count how often the particle prefers to be in one place to another. So the only trick is that we applied also some bias. So we seem, but, but we know how much bias we included because it's simply a harmonic potential. And there is a technique called weighted histogram analysis method allows to remove that potential was from the positions. So we have sampled, let's say, densities, and we recover exactly the same potential as we would as the particle which you've been crossing this range of lines. All right. So this would be an enhanced sampling example. But let's, let's go further. Let's go one step further. So let's, let's look again. The same that we have two states of the system and a large, a large barrier between the two of them. Now we are interested. Again, the barrier is large enough that we wouldn't cross it just spontaneously so we cannot obtain free energy differences just just by pure Sam. We are also, let's, let's formulate the question in the phone way that we are not interested in the height of the barrier. We are just interested in the difference between GA also free energy in the state a and the difference in end state. For example, it could be timing. So the triangle binds to this backman and and becomes a bound ligand bound square. So now we, we could of course do an umbrella sampling, but that would be computationally very expensive and difficult to converge. The question becomes actually somehow learn how to transform this triangle into the square. Is there, is there a technique and this is exactly the alchemical. So let's go now a little bit into the details of that. There are several flavors of the chemical approaches. So here I'm showing I replace the earn now with the, with this ellipse where our question is, can we somehow transform the ellipse triangle and learn what the free energy difference between the two of them is. And there is a way we simply so ellipse is this Hamiltonian. So the potential of the system, which governs the, yeah, the dynamics in state a and potential of the system in state B. All right. Now we can construct a high tone in by simply come back to them with a coupling parameter. So it could be just let's say one my times Hamiltonian a plus lambda Hamiltonian be just a simple linear combination of the two Hamiltonians and control this from the parameter just control it in the simulation. Now, if we very, very, very slowly drag this parameter lambda from one state to another, we can at every point in time we can calculate the partial derivative of the of this combined with respect to lambda. This is the, so the derivative of Hamiltonian with respect to a certain parameter is a force acting along that along that. That coordinate so in this case force along our chemical lambda parameter. And now if we integrate a horse we get work in this case if we do it infinitely slowly. We did the work we don't we don't dissipate anywhere. It becomes the free engine different. And this technique is called thermodynamic integration. All right. So is there another approach and yes there is it. It is a different to consider exactly the same problem it's called free energy perturbation. So for free energy perturbation, we consider system we can simulate the system in state a don't do any perturbation, nothing so far in state B. Okay. So, when we simulated system. We extract the coordinates from the state a. And, and evaluate them with the Hamilton state a. But also we do the. We do the following trick. We take the same. From state a play them also with the Hamiltonian of state B. And now there is a relation the known derived by 20. It's called free energy perturbation that allows to relate the difference between these two Hamiltonians. And their average to the difference, we can also do exactly the same with state B. And it should, it should also come out exactly the same. In state B. Or not evaluate them with the Hamiltonian of state B. So it's native one and the foreign Hamiltonian of state. And their difference in the two Hamiltonians. Exponentially averaged will give us the engine difference. And does it work. Yes, it will. Only friends between the two. Hamiltonians is very small at the order of thermal fluctuations, but usually much larger. To the system where there is no overlap between the two so these two points would be very far from one another but what, but then we can do the trick. Let's simply start putting intermediate states right so we don't directly calculate Hamiltonian and be we divide in the subsection so yeah, XYZ and so on, small, small perturbations, and we do exactly the same math exact. And then we do the simulation intermediate values and collect them into one delta G afterwards. Okay, so this is pretty much a perturbation. And the first conceptual differences between the NTI, they both report on the same free energy difference in the end. But they have different strengths and we FEP is sensitive. In fact, lambda scheduling. Lambda stratification. While TI in principle would be giving a smooth transition, but one is to integrate over over work, work value as you can see, and get the lambda curve and this of course then also FEP would require some equilibration for each and every window and requires one to be always at equilibrium in each and every window and sufficiently converged. So this can be confidential very expensive. But the TI principle relies, or grows standard TI relies on the fact that the transition is always at equilibrium, but this is an an assumption, right. Therefore, there is some certain that the Hamiltonian lag or always introduced work dissipation with this method. So the FEP exponential versus direct calculation for as I already mentioned is actually direct calculation that requires some numerical integration then. And we have more flavor is the equilibrium free energy calculations. Let me also highlight those. So you already saw this of a thermodynamic integration. So we have, we have this way to calculate. In this case, you see, I would double this means that we no longer do this transition from state A to state B, very slowly. So, if we don't do the transition from state A, let's say wild type protein to the mutant protein very slowly. When we make a transition we dissipate work. If we dissipate work well, we call it simply w. So we calculated some work, but it's fine. Now, what do we do with that work. Let's now have a look at a little bit a little bit at that concrete example that I'm sketching here. Let's say we have a wild type protein simulation related very long at equilibrium. We didn't do any magic there. And we made very many transitions from one state to its mutant version. Transitions we calculated this w with exactly this equation that I'm showing you. Now we call values and build a history. This is the blue histogram. Then we do exactly the same but in the opposite direction we simulated the mutant state transitions into the wild type scan. These are the red arrows that we also calculate work values, and we make a red histogram. Now we have problems and they overlap somewhere. And there is a powerful theorem which is derived by crooks. It relates simply probability distribution in the forward direction of work values with the probability distribution in the reverse direction to be different at the intersection point. We can also recover free entry difference this way. Now we dropped the assumption completely require equilibrium durations. Of course the end states these two ellipses like ellipses they need to be an equilibrium but later we don't. So this was the really theoretical part. And let's go now a little bit. Towards the applications. And now you learned a lot about methods that we applied yet, but let's try to bring it to the concrete example. And the example I'm phrasing here is a calculation of thermostability in a protein due to a mutation. So we have the following step, a protein, which can be in two states in this thought experiment. It can be in its folded state and in unfolded state. So we learned that we can extract free energy differences by counting. So let's simply simulate infinitely long and how protein sometimes unfolds, count how many times it is in the folded state, count how many unfolded. Relate these frequencies of the unfolded to the probabilities of the probabilities extract the free energy difference. All right, but this, of course, there is a catch that practically very expensive or feasible because I mentioned that let's do this process infinitely long so it will take a while to reach something right. But let's so let's continue and let's do the next trick. Let's introduce the mutant. So now we have two situations, one wild type situation, and another is a mutant where mutant is folding unfolding folding unfolding and we do exactly the same trick. And now we have systems, which we need to simulate infinitely long. So you may ask, well, just do you made intractable problem twice intractable. All right, true, but now we can that we have also chemical methods, let's do the alchemy now alchemical methods will go in this cycle to draw here, here in the cycle. They will be the horizontal arrows that are connecting the two wild type and mutant in respective folded and unfolded states. So what it means is it means that we are chemically we need to create the Fiancid difference protein in the folded protein and in the unfolded protein, and then from that Fiancid difference. So, in one case, Delta, we recover Delta Delta G, and this Delta Delta G will keep on using this Delta Delta G throughout the practicals and the next examples. This means how much the protein folding Fiancid changes upon mutation. So if Delta G is negative, then we notation made the protein fold. Yeah, strong fold more or the folded state stable that then done full respect to its wild type state. All right, so that's all the magic that we have. Of course, these are more explanations. We still need to build a technical practical framework for that for for running these calculations. So maybe you are already familiar with running standard Fiancid calculations or simulations where you can solve it the system in a box at irons and run the simulation. But now we need to do something a little bit different. We need still to have the same capability of running the simulation, but now our system needs to represent both states, the blue wild type and the red mutated state as in catch at the same time, and we need to have a control between the two states. And for that, so as a dissimulation, but we need a patient for that, we have developed our PMX framework for that. Of which I will talk exactly which which I will discuss a little bit more in detail, but I'll mainly go into the examples showing how we can do what we can do relations. And we'll have a real hands on in the next session on to to where I will show happening to the structures when we do this. When we do this diesel chemical transitions, what happens to the topologist exactly results in and so on and so forth. So we'll now let's have a look what we actually can achieve with the diesel chemistry approaches. So I divided roughly into three categories. Let's have a look at the amino acid mutations, nucleotide mutations and ligand modifications. I'm changing the system in the questions that we ask here and then and this all can be achieved by changing the term. So the protein mutations and ask, so can we predict accurately how mutations change protein thermostabilities. We took the sample protein very well studied by experimental it, it has been all mutated through and through experiment color the mutated in red, and we simply experimentally it has been mutated by and the folding pharyngeal difference. So we can calculate with those alchemical method that I showed before exactly the same pharyngeal differences and compare them to this. So this is a classical way compared to the delta delta G I'll show a few of those plots so let me briefly describe one of the X axis is a G so this pharyngeal difference in the folding pharyngeal difference between pharyngeal upon a mutation as measured experimentally is exactly the same just calculated so no experimental input just calculation and yeah you see as you see over trend is very, very, there are some outliers there is some deviation, which is below one kilo calorie per mole on average, the gold standard in the field, we are always aiming to reach that standard because we know that below that average error is difficult to force field issues sampling issues and also the experimental error we cannot be exactly exactly on on top of usually, but this limit where that we are able to reach with our methods. You can also change this to protein and I can simply modify thermodynamic cycle a little bit, and all of a sudden, I do exactly the same alchemical mutations but in this case, how, how strongly. I mean I said mutations influence the binding offer. In this case, it's up to to major compatibility complex. That's exposing a path there so I mutated all of these yellow residues and compare them again to experiment. We don't need to the details of this, but it's merely to bring the examples of how these how these collide and again we exactly the same accuracy below one kilo calorie per mole again so yeah let's just look at the left left scatter plot and experiment calculations are very good trend again several outliers we know that they will occur in our calculations and we often alleviate those by sampler or maybe including another force field, but this is a very traditional answer that we expect from. Now again, we keep on pushing this further introducing new questions, and another question could be, could we predict mutation in a protein could be drug resistant. So for that, at first we took HIV proteins as economic. So it's a it's a is usually targeted by drugs in the patients, however, that's what makes HIV so so difficult to treat it mutates, you give a some certain. And then it quickly. There's a few mutations and escapes those drugs are no longer effective, but and it's of course interesting can we rationalize it can we which which I the mutations are making these effect having these effects. So we this time we again thermodynamic cycle where we effect of a mutation so blue versus red, but in this case, not on the folding it before but on the. So, holo versus apple states of the system, and we took all the known or major known. And we used to treat HIV, see that again our experimental versus calculated free energy difference correlates very well, we don't have a perfect. We don't have a perfect. Let's say so we do have a little bit of an offset, but we're very happy because we can distinguish a strong resistance. Low resistance mutation in the drug bindings so we can already have a strong predictive our approaches. We even pushed it one step further, so it is quite intuitive that if the mutations in the active site so the, the previous mutations that we broke. Yeah, if you mutate something in the active site well it will clash with the ligand and it will have a. Direct effect. It's interesting to probe those red residues that I'm marking here that are far from the ligand so they don't have any interaction. And still they can influence the drug binding. So, again, we probed our free energy calculation technique in this. Correlated to the restriction factor which is related to the free energy difference. So to the ligand binding affinity. A very good agree simple we can again discriminate those that will be drug resistant from those that will be less drug resistant. A strength of these molecular dynamic simulations is that they, once we now we have established that we can a accurate predict. We actually have also access to the trajectories and therefore we can understand the mechanisms of what is have the system so I highlighted now the two residues. Well, let's say this is one recipe because it's a homo. We looked closer so why is this mutation, all of a sudden resistant to the drugs in HIV. And it appears that this mutation, it's a little bit to another hydrophilic smaller with residue mutation losing to the alien. What happens there, once we remove losing there. So we replace the alien, all of a sudden, there appears more space in this region of the of the protein. There isn't all of a sudden us in lysine can move closer to us party and form a soul bridge. All right, this happens. All, of course, the loop on which this lysine sits. When it shifts a loop, it destabilizes is indirectly actually transfers the effect of the mutation losing and destabilizes the ligand all of a sudden. The ligand. And the mutation exerts its drug resistant. So, in the end, as a very nice. Well, maybe a nasty mechanism of HIV nicely. It's by the molecular dynamics simulation. All right, we let's move on so I promise to show also something different in terms of what the biomolecules we can treat we can also mutate DNA so we can ask the following we identify how DNA nucleotide mutations would affect DNA protein binding so again I'm just more into the thermodynamic cycle in this case mutating DNA and I'm asking, will the mutation make the binding to the DNA and protein stronger or weaker. And for that we collected very many DNA protein complexes to to thoughts that these are very complex is as well, including the endonucleases and transcription factors, various complexes to look at the correlation. Very similar answer slightly slightly worse and quality than for protein mutate. This could be due to the due to the fact that. Yeah, maybe DNA force fields are not so advanced, not not so often, and therefore not so refined as protein force fields and also experimental data was from very range of sources so. Overall, we still can get a very good predictive accuracy for DNA mutations as well, and we can then further further questions now we have a good message to determine the differences. Can we do something what is often done experimentally so experimentally from, let's say, random binding essays, it is possible to define DNA binding profiles. So what people do they just allow random nucleotides in such an essay bind the random DNA see to the protein and countless from their experimental outcome they count how many times let's say I saw. I didn't in the positive or how many times I was going in a position seven and from these counts, it is possible then to reconstruct such a low thought that tells us what exactly nucleotide preferences are for every position when it's bound to the protein. We can we these established the counts are directly related to the well counts are also probabilities of finding some given position, and this again nothing else but the three energy difference, so we can again. Reestablish this connection between the energy differences which we can calculate the and the and such a probability probability profile. Here I'm showing several such profiles, and the just just by eyeballing I will explain in a second what they are, you will probably see that there are all have the same teach just have small differences between them in particular in particular features they do differ, but they're. The major features are the same, and now the top profile is the computational scan is from our computation all the one to these so for bottom rows are different experiments. Either it is a select six or or within binding my primary experiment. What I'm trying to illustrate here, I also have a quantification of this. Just I find it to see that experiments do have uncertainty, and this uncertainty is makes it a result virtually from the calculation results so in principle, what we compute we it falls well within the of the experimental measurement. All right, and with this we go to the last part for the for the presentation today. So we also can do arguably the most lucrative part, we also can do the ligand modifications, let's say, we are asked. What is the different ligand binding affinity for the red ligand and the blue ligand we construct the following terminal. And now we do the same transition just in this case for the ligand binding, not for them in acidification, not for the nucleotide but for the modification of the. Here I'm waiting with more detailed time cycle we don't need to modify the whole leg and we can just change one particular substitution. Experimentally, often it is difficult because you may need to design a completely different synthesis pathway for those. So it is difficult to expensive also, or maybe not even feasible to quickly get an estimate or so the synthesis of the molecule of the molecules, but we can quickly test that. And yeah, it's been it has a long history because it's such an approach with for the pharmacy industry because it would immediately have consequences to the and the lead optimistic. And the, of course, it has been advertised that this is possible already here I'm showing in 1987 so more than 30 years ago, where people show just on on several molecules that yeah, it works. You can give accurate answers with all these flashy high promises it took it was maybe just a lucky coincidence and and the long time until the field really matured to the to the level where it is now applicable with a routine drug discovery pipeline. 2015 paper where Schrodinger incorporated the the company showed that they do have now access to the routine calculations and they provide them, they established this new state of the art calculation pipeline. And yeah, we wanted to see our PMX and drama can also reach the same accuracies as this Schrodinger corporation, and we made our own application by collecting a large number of pharmaceutical relevant protein ligand complexes and computing simply computing the binding free and we can compare them directly to the, what would we get if we were to use this Schrodinger's expensive commercial see that we get on the right side it's again, as usual, experimental versus calculate the Delta Delta G's for in this case for ligand binding to the proteins and the in terms of the average and certain average unsigned error, we are again in the regime, identical correlation we are again within the uncertainty limits from one between the two methods, you have slightly larger error. And this is mainly because of the methods that we're using to calculate the uncertainty we simply try not to estimate the uncertainties as we run independent repeats from our populations. But otherwise, we are able to reach the same factors as the commercial. And we also can do now, the last two minutes I just want to show that now a talk about mutating something so mutating one amino acid to another mutating nucleotide one to another or changing a small part of the of the ligand, but we can also principle we can do absolute binding operation. Let's say we don't want to mutate just or modify this a part of the ligand we can in principle disappear. Alchemically, just modifying the thermodynamic cycle a little bit and it requires some other computation, some other theoretical and computational considerations, but in principle if we ask the question, can we bind, can we bring this from, from solvent so from water into the binding side of the protein. It is this transition of binding is it's computation challenging but we can do it also all chemically we can disappear the benzene, we can restrain it so place it into the pocket. And then, by removing the restraints and taking their contribution into account a couple system, and we cover exactly the same delta G, but in this case, it's not a relative but an absolute binding. So we, it is also possible. We have probed it in a large large scale scan. So if I just show, we selected from our previous investigation a subset to have many values to play with, we also can recover a very good agreement with experiment there is there are more of the red points that we saw before, but in principle that overall accuracy is very, very comparable so it is also feasible, just the, the, the bottom line that they wanted to bring today. And, yeah, I would like to thank everyone who was involved in studies and tell. Yeah, also other findings, and I'm ready for questions. Thank you because I will encourage everyone to write your questions in the chat. And we can take it from there. So, have a question from either how much computational spend time are needed for PMX of a protein complex. For instance, I guess the question is if you have complex and you want to calculate the absolute binding energy interpretation of the question. Okay, let me give a bit of an overview so now these calculations that I showed all of using non equilibrium free energy calculation protocol. So, the timings that we would need for that are approximately say, in orders of up to 100 nanoseconds per PNG value in total. So, irrespectively of the of the question that whether it's protein complex or protein ligand complex. In total, it would take, let's say 100 nanoseconds or seconds to get the things that I reported. Now, it of results in a different user time needed, because the larger systems if you're interested in protein protein complexes will have many atoms you will. You will have a lower lower simply lower nanoseconds per day output for that. Yeah, but but that's probably another question. Is there a big difference because if you're in a small legal compared to this much larger molecule from a complex that it will introduce additional. Yeah, that's also a good point. Of course, the perturbation size also matters. We always play an perturbation that are not as small as possible because then we simply retain the system as close to equilibrium as converge quickly. Of course, for the absolute free energy so I only touched very, very lightly on that, but those would be much more to converge them one needs a 10 times longer something than them to converge relative changes that's why relative changes are so they are easy to. And the perturbation sizes of. Yeah, I don't know up to up to atoms should be should be easy to punish. Thanks. So there's a question from Gregor, who's asking whether accuracy compared with MGB SA or MMP BSA. Yeah, certainly these these methods of chemical math are more accurate rely on this assumptions that the that the approximate methods. Also, yeah, we don't have a problem of incorporating or combining add adding with the anthropocontribution. Say, you you compute something you fit the curve. So it's already cheating is involved and then when you add now a little bit from another method and this Frankenstein of course can be fit into a good agreement. But it's by no means robust and rigorous. For question. You see difference in performance of the various force fields that you have used in the. Yeah, that's a very good. We do see difference with, let's say, probably amber for the force fields and charm family for our performing best in our experience. Maybe PLS is. This is a little bit less accurate, but we are always using the non commercial PLS version. Yeah, publicly available. And what the interesting thing that we've noticed that the force errors usually cancel outs force fields do make errors. But they are often in different directions or in different parts of the mall than they reduce one another. Mainly, I could explain this by the fact that different force fields molecular mechanic for currently have very simply simplified forms. So there is only fit with such with such high highly restrained functional forms. And, for example, amber is trying to the optimally the electrostatic potential surface representation of small molecules. At the same time charm is not trying that and to optimize the the interaction with water for small molecules and coordination with the water. These two may not be necessarily compatible in one single force field but if you were to simulate to obtain else with two different force fields, have a much more accurate representation of what's overall happening in the system if you're if you're simply able to find that console both of them. It's difficult to say how to find this consensus, but for free energies, it's very trivial in principle, just a value so you get one value from amber. Another value delta G from charm, and we noticed that these two force fields are very well compact simply calculate average of those. This will be always at least as accurate as the more accurate force field alone. Thank you. We have another question regarding outliers. So in the examples that you're showing there were outliers, but do you that people validate or benchmark results for every application today? Yeah, certainly. It's always very good to very good to have some experiment data on the system or a similar system to compare to before starting to make predictions. So there could be, of course, with either with the force field or with a particular setup. For example, just from the personal experience, always an issue if there are additional factors involved, simply the accuracy drops significantly. But if you have a handful of data to compare, it's always good practice to establish the relation. So what will you expect from your prediction? Sorry, I was muted. Thank you. So I don't see any more questions in the chat. So now it's 1030. So I suggest we take now the half an hour break before we continue with the practical demonstration at 11 o'clock. So thanks everyone. We'll have a break and we'll come back again in 30 minutes.