 So my name is Cristian Michaletti. I'm part of the faculty here at CISA, a colleague of Ali. And it's a pleasure to be with you and to share some work that we did in the past few years trying to give comprehensive perspectives on a problem that is ubiquitous when you're dealing with biomolecules that are flexible, usually densely packed as they are. Typically think of DNA inside a cell, whatever cell, a bacteria, eukaryotic one, even of the simplest possible organisms, which are viruses. So inevitably you end up with lots of entanglement. What are the implications of these entanglement for the biological processes of these long biomolecules? And to what extent you can learn about the properties of the molecules in experiments. So you want to identify a statistical mechanical approach to characterizing the entanglement that spontaneously arises in biomolecules. And this is what we have been doing using coarse-grained models and STATMEC. And the other flip of the coin is instead of to look at entanglement, let's say knots or links, that you can produce in a synthetic way. So instead of relying on the entanglement that spontaneously arises, you wanted to design that. So end up with special type of knots that you are interested in, not the casual knots that you end up in your earphone cords when you walk with them in your pocket for a day and then they're full of knots, but these are statistical. They're usually not the knots that you want, not in the positions that you want. So I will try to give you a physicist and STATMEC perspective on the problem. Probably a good way to introduce the problem and to quantify a little bit what I've been saying in a hand-waving way in the introduction is to consider the type of packing that you have of genomic DNA across the spectrum of living cells. So in eukaryotes, you typically have meters of DNA that are packed in a nucleus that has a transverse size of about 10 microns. Then you go all the way down to bacteria, you have millimeters of DNA in a micron-sized cell. And if you got the lowest possible level, a level to which you can dispute whether you are really dealing with living organisms in viruses such as phages, you have microns of DNA in a small container, a protein capsid that is typically about 15 nanometer in diameter. That is for the smallest viruses that you can have, phages in particular, which are viruses that attack bacteria. So a very early view on how DNA is organized at such scales is provided by the beautiful cryo-EM picture that you see here on the left that where people, for the first time, they managed to take cryo-EM micrographs. That is, you take tomographic cuts of your frozen viral particles, you measure the electron density. And by taking many cuts along many different directions, of course, from different viral particles, then you can use the theory and computation to reassemble all the electronic structure to come up with an average electronic structure that tells you how DNA is organized on average inside each particle. And as you can see at the bottom of this picture here, you can see that the DNA is, you can neatly tell, you can tell that DNA is organized in neatly loops or a spool, if you wish, that is a coaxial. So it's a coaxial along the axis of these viral capsid. However, one thing to bear in mind is that here what you see is the average DNA organization across many different particles. So you are bound to overemphasize the order, order the packaging of DNA inside. And so really how DNA is organized inside each of these particles can be different, can be disordered. That is something that you cannot really probe yet. An indirect insight into how DNA is organized inside. However, you can obtain from a very different perspective. People like colleagues based in Barcelona, in particular Joaquim Roca, have been able to develop over the years some very ingenious methods where they managed to get the DNA packaged all inside the capsid of the virus. And then it so happens that if you choose correctly your virus, the two ends of the DNA of the DNA strands are complementary. So the DNA is double-stranded. So it's the double helix. But at the very end, it's a single-stranded for a short stretch, a single-stranded and the two ends are complementary. So when these ends have the chance to meet inside the capsid, they anneal, they circularize the molecule. So instead of having a linear molecule, now you have a circular one. So if you happen to have any type of knots formed in there, it would be permanently trapped by this ligation. And then if you remove the capsid and run the material through a gel, you see the formation of different bands. So this is a technique that is called gel electrophoresis is these typically used to separate molecules of different lengths. So it works by preparing a gel that is very dilute. So the gel you should imagine has been like a wire mesh. So an array of obstacles to your molecules. This array of obstacles presents some entropic traps for your molecules and people typically use it to separate DNA of different lengths because if you put an electric field, you know that DNA is charged, you put an electric field at the two sides of the gel, you can make your DNA filaments migrate. And according to whether your molecule is small or large, they will migrate with a different effective velocity because they will be able to negotiate the obstacles of the gel to a different extent. So typically you use this technique to separate molecules by size. But here, though the particles of viruses have DNA of the same length and still you see different bands in the gels, you can see different spots, they are not separated by lengths, but what distinguishes one from the other is their topology, is they're not tight. How do people know this? Because over the years, people very carefully have cut out excerpts from this gel, they recovered the molecules in each of these bands, they coated them with proteins to make them thicker and large enough to be discernible by AFM microscopy. And with AFM microscopy, people have been able to observe and ascertain that each of these spots corresponds to a different topology of DNA, different nodes. So there are very different layers of interesting messages that you can see here. One is that you, and I would say the most fundamental one is that you find out that almost all viral particles have unnoted DNA. So the number of viruses that have unnoted DNA inside is less than 5%. Not only that, but if you look at the type of nodes that you have, it's a very special type of distribution that is very unlike the one that you have in random polymers in equilibrium, or as I mentioned before, in your earphone cords, when you walk with them the whole day. So these topological fingerprints are a robust feature. It doesn't really tell you how the geometry was inside, but it is reflective of how DNA was organized inside. And it's very robust. Topology is not geometry, it's very robust. So these are very valuable information that you want to be able to reproduce with the theory and computation. And so the question is, these nodes, what do they tell you about how DNA is organized inside? Well, here I don't want to give you the fine details of a story, I just concentrate on the broad picture so you can understand at least what is possible, what results are known. So the punchline is that if you create a sufficiently detailed model of DNA, then you are able with simulations of the DNA packaging inside the model viral capsid, which we treat as a sphere, you are able to reproduce the node spectrum. And only if you get the correct ingredients, and these ingredients are, first of all, escluded volume interactions, of course, you need to treat your chain as a thick chain. Then you need to take into account that DNA is very stiff on the scale of the viral capsid. The persistence length of DNA is a 15 nanometer. The thickness of DNA is a 2.5 nanometer. The persistence length, I remind you, is the arc length over which you pay one KBT in order to bend your molecule. So imagine your molecule is very thin, 2.5 nanometers, and you have to pay KBT in order to bend it by one radian over a length scale of 15 nanometer, which is much, much longer than the diameter, it's 20 times longer than the diameter. So essentially the DNA behaves almost like a steel, a thin steel cable that is very thin. And despite this, you have to pay a lot of energy in order to bend it over a size comparable to its diameter, really a lot. And so these are two key ingredients, but these are not sufficient. If you want to reproduce the node spectrum that you see in biological samples, then you need to take into account the double-edical nature of DNA, which is such that if you tightly press two DNA strands, one against the other, they don't want to be at a random angle, but because they have the helical grooves and you have the charges of the DNA arranged the helically along the DNA contour, the two contactless strands want to be at a finite angle from each other. If you take into account these organization principles in packaging simulations, then you can match very, very well the distribution of nodes inside viral capsules. Not only you can account for the abundance of nodes, but you also account for the different relative population of nodes. So in this way, you have a validation of how DNA is organized inside. And then by looking at your molecule, you can have an idea of how the DNA was actually inside each of these viral particles. Now, a more fundamental question, however, is this one. Since we know, we know, not from the models, but we know from experiments that most of the viral particles have a noted DNA, the question is, how come that you can afford to have a noted DNA inside and still the DNA is able to be ejected through this very narrow channel, a channel that is narrow enough to allow only one portion of DNA to go through and not several filaments. So the situation is like, imagine that you have a complicated node here, and then I want to eject these through an aural pore. No, I don't know if you can see my camera. The question is, how come that I can get it out that the virus is able to eject it without jamming the pore in this ejection process. So if I try to do it with this rope, I'm not able to get these through my fist because here there is lots of friction that develops and the knot tight ends, I cannot get it out. How come that we know the DNA is noted and still is able to be ejected from the pore? The problem is also relevant for another context, entirely different, a technological one. Nowadays, there are chips that you can buy that will sequence DNA using solid-state nanopore translocation. So the idea is the following. And it goes back to a seminal idea put forward by Deemer, I think at the end of the 80s, but only let's say in the last 10 years, this has become a reality. Imagine that you have a very narrow pore in a slab. It could be a biological pore, but you can do it in a solid-state slab. You do a pore with a very thin diameter, a diameter comparable to the thickness of the molecule that you want to study. Let's say single-stranded DNA, just one filament of DNA. And then because DNA is charged, you put a potential difference across the two sides of your pore and the DNA will be sucked in and will go through. Everything happens in the presence of ions in solution. Now, as the DNA goes through, if your pore is narrow enough, you can measure the current, the ionic current that goes through. The ionic current will be modulated by the obstruction of the pore that you have. Whether the pore is completely filled or it's completely empty or in between, you will have different levels of the current. So by measuring the current, you may have the hope of being able to tell what nucleotide is passing through at the moment. And this is in fact what it can be done. As you can see here, you have as a function of the position of a DNA strand going through the pore, you have the different levels of currents that you can see. And you can see that there are about four different levels of currents and they correspond to the four different nucleotides. The situation usually a little bit more complicated because your pore is a little wide, is a little long. And so you have more than four levels because you measure properties of two or three bases at the same time. But the idea is the same. Like just taking a simple measurement of current without reagents, without amplifications like in PCR. So it's a very cheap technique. You are able to profile the chemical identity of the sequence just by knowing what is the current. Now the issue that crops up also in this case is what happens when the filament that you are fishing is noted somewhere, because it's bound to be if you have long filaments. And then you try to pull it through the pore and it's going to jump the pore presumably. As in the example of this force of translocation that I'm doing here. So we got intrigued by the problem and also its connection with the viral case. And so we wanted to study it with models with the idea of telling experimentalists the following. We wanted to identify the length of DNA stretches that was safe enough to be driven through the pore without getting jumped because of being spontaneously noted. So if it is short enough, it will not be noted with high probability. So what is the safest length that you can measure? And let me give you, since you are mostly physicists, let me give you take this opportunity to give some background, a simple background on the problem of polymer translocation, which is a fascinating problem. Actually, we had a hybrid workshop on that for an entire week last week. It's an extremely active area. So let me give you the basics of the physics because I think it is something that is worth knowing about. The problem is the following. I'm sorry, can I just interrupt you one second and ask a question? So this, maybe you said that name is this nanopore sequencing of DNA. So the advantage with respect to that data already many existing techniques for sequencing is just the fact that you don't need PCR to verify or is there something else? It's very cheap. You don't need reagents. You can do it in parallel. On a little chip, you can have thousands of these little pits that you can draw things through and you can measure uninterrupted stretches of DNA of the length that you want, the length that you can manage, which has been constantly increasing instead of having to chop it up and then put all the pieces back together using a software, which can be a problem in regions that are highly redundant like central nears of chromosomes and so on. Okay, thank you. So coming to the problem of translocation, here what you see, let me show you the phenomenology first and then I'll tell you a little bit about the basics of the theory. This is a chain. It's an unnoted chain. This is a chain of 15,000 bits. So it's a model chain. There are 15,000 bits. So it's very long. It is fully flexible. It is colored from which shades, color shades from one end to the other so that you can see somehow have an idea of the sequence. And it is charged. It is driven through an anopore. The anopore is here. It is driven by an electric field that is applied only here, where my cursor is. There is not an electric field that goes all the way through the simulation cell, only here. Now I let the simulation evolve and then I will play it again. So to point out the physics. You see that now we have a global that is much denser that we started with. This is not because we have a bottom here. You might think, okay, there is a bottom you cannot go beyond. No, it's not the case. Let me start again. So this was on an equilibrated chain. Let me backtrack a little bit. Okay, so this is the equilibrated chain. This was in equilibrium. It has a certain size and the size of the chain scales like the length of the chain to a power that is called the new, which is about 0.6 in three dimensions. I believe my colleague, Angelo Rosa, yesterday, you heard about it when he talked about chromosomes. This is the typical, it's called the metric exponent. But as we are driving it out of equilibrium very fast in the other side, when it goes to the other side, it does not have time to relax. And therefore it is much more compact. Okay, so this is first of all, an out of equilibrium process, which is very interesting. Out of equilibrium stuff make is one of the most active areas of research. But then the thing that you see that is going on here is that you see that there is a longer and longer portion of the chain that gets rectified, gets linear. In fact, what happens is the following, the out of equilibrium disturbance that you are applying here at the port gets propagated through the chain, through the backbone. And it is like when you undo, if you wish, a sweater now knitted with wool, you try to pull it and then you are rectified longer and longer stretches of your molecule until you completely rectify the chain, which meanwhile is translocated, oops. And once that is fully rectified, it goes through extremely fast. The interesting thing, so here I'm giving you some sketches that you can use a scaling argument that will tell you that the time that you need to translocate the chain grows with chain length, with a power that is greater than one. So naively, you might expect that if I take a chain that is twice as long, I will require twice as much time to translocate it. No, it's not the case. You require much more than that. It is actually a process that slows progressively down. And this is because you're propagating your tension front across a chain that is embedded like a fractal in three-dimensional space and the fractal dimension is new. So it's a diffusion along one chain but embedded in the three-dimensional space with a certain fractal dimension. So it's a complicated process. And you end up with this mind-boggling result that the translocation time is nonlinear as a function of chain length. This is what theory tells you. And in fact, this is what simulations also tell you you need to be careful in order to be asymptotic but indeed the exponent that you can see is very close to that and definitely is not a linear relationship. So I try to give you a flavor for the interesting physics that goes on in the translocation process but the point that I want to emphasize is that all these theoretical arguments are necessarily for unnoted decent angle chains because there is no way that in theory you can use paper and pencil to come up with expressions that generalize to notes. What happens if you have entanglements there? And this is where simulations come to help. And so I'm going to show you what happens when you translocate a noted chain. So this is a chain. It is noted. The note is in the red region. There are, we have developed algorithms that will identify the noted region for you and if you are not convinced that there is a note what you can do is you can just pull the chain. You can do a simulation and if you pull the chain indeed you find out that there is this type of note which is the so-called Savoy note or figure of eight note in that particular region there. So what happens when you translocate the chain? You can try to take your bet. This is your noted chain or our noted chain and this is its translocation process. It goes through. No problem. Okay. So when I saw this result I was very surprised. First of all, I looked at the numbers in my data files and so I thought something had gone wrong during the simulation. Maybe we had a crossing. We got rid of the note for some reason but no, this is not the case. And in order to convince you of that I'm just showing a close up of the same simulation but taken close to the port now. Now I zoom in on the port. So the note is initially very up above my screen. And as I started the translocation process. Okay. Now the translocation process has started. It goes on. Now you see there is this blob here. This is the note. The note was initially far up and then as we pull the chain because we have this tension that propagates the note of titans gets squashed against the poor entrance. It stays there, stays there, cannot go through. It would like to go through but the poor is too tight to let it through. It stays there but you see what happens the chain is able to slide along the noted contour and pass to the other side. So this was very surprising, very surprising in a way difficult to accept. But then of course, if you was that you have the result so you see I'm completely honest about this. Our initial goal was to tell the experimentalist which lengths were safe to process in order not to incur into notes. And then we found something very serendipitous that even if you have a note, that is not a problem. Why is that? Now that you have the benefit of looking at the structure you understand what is going on. Essentially in the noted region where I was zooming in the beads are pulled against each other but to some extent the chain is not very, very tight yet. So the forces that I was applying were sufficiently strong to tighten the note but this tightness was somehow counterbalanced by thermal fluctuations that opened up the note very frequently. And so the chain had enough slack room to slide along itself. Now that you understand this you may have the idea and this is what we were inspired the next to apply a much higher force. So a much higher force should not allow the noted region to breathe as much under thermal fluctuation. So the beads would be tightly pressed against each other and in fact the note now does not go allow the chain to translocate. Now you see the note is tightened, it stays there would really like to enter and go to the other side but it cannot but now the chain is too tight to breathe because we are pulling almost 10 times stronger than before and now the note is not able to pass because the chain is not able to slide anymore along it's not the contact. So at the end of this process essentially we can recalibrate our intuition from the macroscopic scale where we have lots of friction to the microscopic scale where the friction is less extreme and essentially everything is nicely summarized by this slide here which tells you that even if you have a noted chain if you pull with a low force it goes through no problem almost like an noted chain you pull a little bit with a slightly higher force it goes through faster as any chain would do but then if you start applying higher and higher forces eventually you slow it down until you jam it completely. So the more you want the less you get if you want to remember this result in a pictorial way. And these can be generalized I don't want to get into unnecessary details but this can be generalized holds for different type of notes there are no commutative properties if you have one note after another note the translocation properties depends on the order in which you encounter the notes there are different notes families all these is actually not only a curiosity but it's actually relevant in connection with the problem that we looked at because in the bacteriophages there are different families of notes that occur spontaneously and now we have the insight into wow why it is actually possible to be highly noted and yet being capable for the DNA to be delivered through an aropore that is not large enough to let the note goes through if you compute the pressure holding the DNA inside there and therefore the ejection force you estimated that this force would never be enough to jam the translocation process. So there are various reasons included the fact that notes are under confinement are delocalized and they are not tight but even if they were tight the ejection forces would not be strong enough to jam the chain. So we have resolved in this way a conundrum that had been in the community for a while. So let me check how much time I still have 10 minutes, right? Ali? Yeah, that's correct. Okay, including questions or not? Including questions. Including questions, yeah. Okay, so, okay, I guess just to for the sake of having a complete story maybe I will just talk about complete this part about translocation and not cover the one or synthetic notes. Very recently, there have been some experimental breakthroughs that have allowed the people to use the same setup that I mentioned with very narrow pause to do sequencing and use that instead to detect with unprecedented details the amount of notes that you have. Why is that interesting? Because the technique that I mentioned here the one based on gelatophoresis has some intrinsic limitations. You can use it for DNA stretches of up to 10, 15 kilobase pairs, thousands of bases, not more. The reason is that the longer is the DNA the larger are the electric forces acting upon it. And if you keep increasing the size of DNA eventually the DNA will snap. And so you have to stay below a total contour length if you want to use the technique at all. So people are really blind as to what are the incidents of notes in lambda phage viruses which have a DNA of 50 kilobases for instance. So this technique will not be confirmed. What other techniques are available? Well, zero until about five years ago but very recently about five years ago Kisdeker and coworkers introduced a very elegant technique that uses the same principle of nanopole translocation to detect notes. And so let me tell you how we used COSYR models to complement the insight that you can get from these experiments. First of all, the phenomenology. They use a very wide pore, 10 nanometer in diameter. I told you that DNA is a 2.5 nanometer in diameter. So these are pore much wider than your rope. When the filament goes through, the pore is partially occupied. So you go down your current level by one notch and then you go back to the baseline level. Your string of DNA can actually enter the pore in a back-folded way. In this way, it starts by, the current goes down by two notches initially. Then it goes back to one when it is occupied only by one filament and then back to the baseline level when it's done passing through. And then you have signatures like these, which I ask you to think about it for two seconds and try to explain. We start from the baseline level, go down by one notch. So there is one filament inside. And then suddenly we go down by two notches, go back to one and then to zero. Or same situation here. You start to go down by two notches immediately. So this might be a situation like this one here. And then suddenly after having gone back to one strand, you go immediately down to occupation of three strands. So go back by two notches and then what? What is happening after the blue? And the only way to make sense of these signatures is to assume that you have a knot there. And these signatures you find in linear DNA and you find in circular DNA where knots are permanently trapped. So you cannot really see the knot, but it's the only way to make sense of such signals. And this technique allow you to answer a number of very interesting question. Well, first of all, you do counting. You can see how many of these instances you have, which allows you to count how many knots you have, the abundance of knots that you can get also from generator freezes. But then you have other information like when I had the signal of a knot passing through, when was that occurring at the beginning of the process in the middle, at the end, uniformly in between because the knots are expected to be random. And also what is the duration of these signal that you have the knot passing through? Is it brief? Is it wide? Is it a tight knot? Is it a broader knot? So these questions are all questions that you can answer, at least in principle with this technique. Well, first of all, regarding the first one, measure the incidence of knots. So this is what they were able to measure. They measure the spontaneous incidence of knots in DNA of up to 1,666 kilobase pairs, sorry. And with generator freezes, you are stuck at 10 kilobase pairs. So you are about here. So that's an order of magnitude improvement. And I don't think that is really an upper limit so you can go beyond. And then there's also some interesting features like the statistics of when you see the signals due to the knot is skewed towards the late passage, late at the end of the process. And then most of the passage events are very short, very short to the point that if you estimate the knot size, that would be tens of nanometers. So that's very tight because the persistence length of DNA is 15 nanometer. That means your knot is much smaller than the persistence length. So it's very, very tight. We tried to, am I on time? Ali, I don't know if I heard. Yes, you're fine, you're fine. Okay, so I'll try to wrap up in a couple of minutes. So we use a model, so that is quite detailed. So a model that accounts for the double medical nature of DNA and also for the possibility for the strands to open up. Because we assume that if you have a topological entanglement doesn't may actually snap or cause a bubble in the DNA to open. So we didn't want to miss that. It didn't come up to be an issue at all. So this is a model of the double strand DNA. So it looks like a filament, but it's actually the whole double helix there with the two filaments. The knotted region is red. You can see what happens. It tightens a lot before entering. So it makes a few attempts to enter the pore, and eventually it goes through and when it goes to the other side, it opens up. So let me show it again, because it clarifies a few things that were not clear from experiments. This is a knot in equilibrium. By the time that it reaches the pore and then you measure it, the equilibrium properties of the knot are gone. So what you measure, unlike the expectations that experimentally said, is not indicative of what the knot was in equilibrium. It's much tighter. There is no weight. So by measuring it, you disturb it. So it's not a delicate procedure. And then while experimentalists use currents, we can measure the occupation of the volume, which is about the same thing. So we can measure when the events occur, what is their duration, and what we... Okay. And experiments saw a skew towards the late passage events. We see the same skew, and this is because the propagation of the tension front always tightens the knot before reaching the pore at the essential crossing that is the furthest from the pore entrance. So even if you start with knots that are randomly distributed on the chain, by tightening it, you're pushing it away from the pore effectively. So this is what causes the late passage events. So this is something that you can understand in simulations that was not clear with experiments. Not only that, but what about the size of the knots? Well, we find out that about in half of the cases, the knots were not tight at all. The knots were actually occupying the whole region in the sea side, so the before translocation side. And what was tight was not the knot, but only the tight gathering of what are called the essential crossings. So you see, this is a situation that is very different from when the knot is only on one of the two sides of the filament. Here the knot really sits across the two in a very dramatic way. So again, this is indicative of the fact that if you measure the signal, that is cannot really be by itself revealing or what is going on behind the curtains. So this is essentially a push to design, if possible, setups suitable pores of suitable size and geometry, suitable applied forces in order to be able to distinguish properties that otherwise are all lumped together. Okay, so I don't have time to show you the molecular knots. So let me just go to the acknowledgments and acknowledge the people that have been involved in these studies. And I will be happy to take questions. Thank you. Thanks very much, Christian. I believe there's a question already in the chat, Christian. Okay. So, Patricio Barletta, if you increase the temperature, you are able to pull harder. That was back then when you mentioned, hi, hello, thanks for the very interesting talk. That was back then when you mentioned that it was random fluctuations that allowed the knot to relax. Yeah, yes. I would say, in brief, I would say, yes. Maybe I would phrase the answer, a longer answer in a slightly different way, but I think you got the right idea. Essentially, everything is controlled by a dimensional ratio that has to do, that involves the force and the time scale, which is essentially knot side divided by KBT. And so it is this ratio here that determines whether the knot is able to breathe and therefore you are able to get it through, or if it is completely stuck. Right. And in the case where you put experimentals that we're trying to solve, please, in the case where you are in control of the force field, what if you change it back, you switch it when it hits the knot, you switch it back, you let it go up, and then you pull harder if you do that. Okay. This is an interesting question. I think there are groups that have looked at these intermittent mode of pulling, if I understand. So you say, apply a force, zero, apply a force zero. So instead of having a constant force, you do a square wave modulation, let's say. Right. Sinus order. So there are groups that have done that. We have also done it recently, but I think the first group that did it is, Shinchuk, I think, and they saw that that allows you to use, so if you use impulse, that allows you to get the knot through, even using forces that applied at a constant level would jump the knot. Because essentially, when you switch it off, you are precisely giving the opportunity for the knot to breathe a little bit. And so the next time that you pull, if you gave it sufficient time, it would have opened up and you gain one inch and then again and then again. Thank you. And I was wondering, you mentioned, are these knots present in just bacterial phase? No, no, no. Of course not. I think definitely they are present throughout all genomes. And the, so I think bacterial phages, maybe are not even the first system where they were detected in the first place. They are reported in bacterial DNA. So in bacteria, those have been studied really a lot. And now recently, people have been able to devise the technique to detect them in eukaryotes. So I think our knowledge of the abundance of knots in genomic DNA is just limited by the technological difficulties of accessing them. So the same group of Yakim Roka has done beautiful experiments. They, two years ago or three years ago, they in 2018, you look at a couple of nucleic acid research papers, they measured the occurrence of knots in mini chromosomes of the east. So which is eukaryotic DNA with all the nucleosomes, et cetera. Thank you. Yeah, maybe if you can answer the next question. Right, okay. So it is very surprising that not can be resolved even under law force. I would say because of the law force, I missed the sound. I cannot imagine how it comes in energy or entropy barrier, the long DNA. Not sure I understand, but anyway, so the idea is that the reason, I hope it was clear from the video, the knot was not resolved. So it's not that we got rid of the knot. The chain was able to slide along its knotted contour, which is different. And the reason why it was able to slide is because friction at a macroscopic level is not as strong as you see in this piece of rope that I'm not able to get to sliding anymore at a certain stage, you know? And so the friction depends on how tightly your molecule, in this case, our beads, which I remind you, the beads are not there as physical beads. The beads enter through a spherical, symmetric potential centered on the center of the beads. So if your beads have wiggle room because of thermal fluctuations, imagine a bead that has to slide along the contour. It will feel a bumpy ride because it gets in the way of a very scalloped potential, no? Festune the potential due to the interaction of the other beads. But if your fluctuations are larger than the barriers in this washboard potential, it will have some friction, but it will still go through. If you pull very tight, you increase the barrier so much that even if you apply a slope, if you're driving, you're not able to get it beyond the barriers. I hope it's clear enough. Oh yeah, thank you, it's clear. So the sequence slide through the knot, instead, the knot was disappeared before it passed through the... Right, the knot was there, it didn't get unnoted. It was translocating despite being noted. Okay, yes, thank you. Okay, thank you very much. And I guess Christian will be at the gather to this afternoon. We don't leave one caveat. So I've got a commission for an examination at 2 p.m. So as soon as we finish, which might take up to one hour, as soon as we finish, I will join you on gather. So I will not be there immediately. That's for an institutional duty.