 Dobre možeš. Prosto, da boš mi početno, da je Kristia Michela Tiena, organizator in je mi početno, da početno da se početno vzajte in izstajte. Tukaj, to se zelo, da boš o načinaj biologijski sistem, najmaj, replikati DNA, ko je vzal, in generacije superkojljiče začali. Na različenju, da bomo pravati, nekaj, kaj je pravati, kaj je pravati, kaj je pravati. Premač sem pravati na grupu DNA-kromozomnega grupa na Universitetu in Loza, v centru integrativnih genomikov, kaj je pravati v medijsnih biologiji. in bioloži. Kaj recently we became also a part of Swiss Institute of Bioinformatics, which provides the ground for people studying biological problems by computer modeling. So the head of the group is Andrzej Stasiak. We work together on DNA topology and molecular biology and topological problems, such as DNA knots. Well, there are two permanent members of the group, Fabrizio Benedetti and Julien Dorje. There is also one ex-member from the Department of Theoretical Physics from Polytechnic School in Lausanne. So these people co-authored this work, which is going to be presented. So I would like to interest you into the talk with these outlines. So, first of all, I will mention the importance or the occurrence of the knots and links in the biological systems. Then I would like to address further topological aspects, such as topological isomerases, juxtaposition, leaks and gaps and supercoiling. Then I would like to present the computational model of our DNA with some detail, because I want to show how do we simulate these topological aspects, supercoiling and active as we will, and so on. Then I will show some simulations going from the simplest cases of supercoil open trifle knot, which is basically linear chain. Now I will continue through some more complex problems, and finally I will present our biological computational model for anointing and decatenation. And I would conclude the talk with some remarks from this talk. As we have seen during this workshop, the knots occur on DNA molecules. They are inevitable. Formation of knots is unavoidable in long DNA molecules and crowded environments of long DNA molecules, such as bacterial DNAs. They are a result of the action of topological isomerases, which mediate passages between DNA chains. The DNA knots can be also a result of replication, as it has been shown in this work in the Hydrage channel. These knots can be very harmful, because they can create an obstacle for the polymerase, and they can simply cause the polymerase to stall, so they avoid transcription. Or they can really cause, upon tightening of the knot, the mechanical breakage of the DNA. These DNA knots can be very harmful, and they have to be removed as quickly as possible from the molecules. Catenase is another topologically restrained formation of DNA. They are even more regular than DNA knots. They actually, in circular DNAs, they occur always. This is a natural result of replication, because during replication there is, this object is formed, it is co-replicon, and during the replication the DNA has to be unbound and read by polymerase, and so on. And during unviding the DNA, substantial amounts of suprecoiling is generated, and because this is a closed object, this is circular DNA, so this suprecoiling cannot just diffuse away, but it has to be removed by topoisomerase, such as topofor, or agirase. But the thing is that in the terminal stages of this replication, there is not enough space for those topoisomerases to sit on the molecules, so they flow away, and as a result of those remaining turns of the DNA, those two new freshly replicated DNA rings may be cutenated, or linked, or entangled. And also these cutenates can be very harmful for the metabolism of the cell, and they have to be removed as quickly as possible. The cell has this relatively small molecules of enzyme, which the cell uses to manage the topology of the DNA. There are basically two types of topoisomerases, which are divided in type one and type two, based on how many strands they are allowed to pass, so intuitively, type one will allow, topoisomerases will allow passages, or deal with passages of one, or single strand, and topo two will allow passages of this kind, of two strands at once, causing, for example, transformation between relaxed and unrelaxed DNA, suprecoil DNA, and knotting and decatenation. So in this talk, we will be mainly interested in topo three, which is type one, topoisomerase, and about gyres, which is type two, topoisomerase. Ok, so the longstanding question is that how these topoisomerases actually know where to act, where should they take the action, because they are relatively small molecules, and in this crowded environment of DNA molecules it can be rather fuzzy to say where should it make a passage, and if it acted randomly, it would make the problem, or it would make the system even more tangled, even more knotted. So in the work by Ibenko Volokotski, Kotsarelli, and so on, they suggested that there is something smart behind the action of topoisomerases, and they have shown that in their experiment they used linear chains of DNA, and they ligated their ends in a solution, and it produced some equilibrium value of concentration of knots, and then they have seen that when they added topoisomerases, these experiments were made in bacteria as well as human cells, so they have shown that the concentration of knots dropped under its equilibrium limits, so this action of topoisomerases is not random, this is what they concluded. Fadremor, what these authors did on topoisomerases, so they suggested that for an optimal passage there has to be created a juxtaposition, which consists of a strongly benchy segment, and a stretched T-segment, and for the topoisomerases to successfully act, this T-segment, as we passing from this convex side from this bent side to the G-segment, and this could also explain, or this could provide some solution for how this topoisomer is nowhere to act, because in small DNA molecules there is a natural curvature of the molecule, so there is a natural bend from inside, so the molecule or the enzyme knows where is the outside, where is the inside, but the problem was again in the long DNAs, because this juxtaposition should occur in the part of some very large crowded molecule, so it wouldn't, again, if it would make a passage, it would cause the molecule to get more knotted. So there was some missing factor into this, and in the work by Guillaume Witz, Giovanni Dittler, Andrzej Stasiak, it was suggested when they observed these supercoil molecules in Giovanni's lab, and so Guillaume Witz did Monte Carlo simulation, and they found that there was a stable configuration, which looked like this, it was a stretched molecule, and the knot was localized by the supercoiling in one of those apexes of the molecules, and again this conformation or this localization of the knot cause that there was this natural curvature of the DNA occurring, which gave an information what was inside, what was outside of the molecule, so it created this, conveniently this bend region for the topizomerase to sit. Ok, so now I'm going to say again what is something about supercoiling, so this is the picture, which has been shown several times. It's DNA double helix, and supercoiling is a property which directly arises from this double helical structure of the DNA. Unlike simple polymers, the DNA cannot freely axially rotate, because there are double strands, so the rotation is axially restrained. In simple polymers, however, we know this rotational coordinate, which passes through these potential wells and peaks periodically. But in DNA, the rotational coordinate would look like this, when upon twisting of DNA, the energy will build up and it will be stored in the chain. So it can be modeled by this physical, like rubber band. And again schematically, so we have the case of circular DNA or rubber band, and now we are interrupted in one place, but it is still connected. And we twist it, and we introduce the twist, so this is something like active swivel. And when the torsional stress increases, and it eventually causes the supercoiling or making of these crossings, it's called a writhe. Of course, in the case of DNA, we talk about delta twist and delta writhe, because it has some interesting writhe, which originates from this double helical structure. And so the molecule releases this torsional stress by this transformation in the additional level of coiling. Now in biological systems, the role of the active swivel is taken by the type 2 isomerase, called gyarrase. Gyarrase is a special topoisomerase, which mediates passages of the molecule itself, and it creates a strong band and it makes the passage in a close environment of this topoisomerase. So it introduces this kind of twist. Ok, so this is the part before I show the simulation. So I would like to go also in some detail into the model. So as it has been mentioned already, I think by better we are now. So we know the structure of the DNA very well, and starting with simulating the DNA from atoms, it could be very time-consuming, it could be very expensive for computational time if we wanted to study the processes on the scale of biological problems. So there would be moreover, for one turn of DNA, there would be like 600 atoms. So for our plasmid, kilobasper, we would have about 18,000 atoms, and moreover we would like to study the DNA in its natural environment. So it means at least water or something, some water solution. So there would be like other zillions of solvent molecules. So this would be really expensive for computational time. Moreover, there is a wide span of typical time scales of molecular movements. If we started from atomistic simulations, the fastest movement would be bond vibration, which would start at femtosecond scale. Then we would go through angle bandings, on picoseconds, torsional transitions, on nanoseconds, through rep patients, microseconds, slowly moving to this biologically interesting scales, which would be in fractions of seconds. And of course in the crowded environments and condensed system, concentrated solutions, it would get even up to years. So in fact, if we started with atomistic model, it would be very convenient to build the model, to throw everything in the simulator, push the button and see what happens. But this would be wasting of computational time and actually as comparison to this fastest atomistic movement, we would produce a lot of redundant information. We would have mostly hydrogen bond vibrations. So what we do is called systematic coarse graining approach. So we replace some chemical details of DNA in favor of gaining these faster computations. And the systematic, the war systematic such as that we don't do it, just like ad hoc, but we have some system to it. So here we define our bit, which we use to replace some portion of DNA, the size of the bit of course is defined by the scale of the problem that we want to study. So we want to study problems on the scale of the DNA chain, so we have to use this. This is common in our models in literature, so we use a base pair replaced by a sphere of 2.5 nanometers. Then we would like also to have the classical model of DNA also contains this chain stiffness, which we know is about 50 nanometers, so when our bit is 2.5, so this should be around 20 bits, but actually we had to decrease this value a bit because we introduce also electrostatic charge, which comes from the phosphate groups in the structure of the DNA. Of course, this one is screen, so we could decrease the value of the charge and we use the biohukal interaction to model it. And then we adjusted a little bit this parameter of bending parameter in this chain stiffness. Now, this would be the bit of chain, but this still wouldn't store the information about the torsion, about the twisting, so we have to add additional bits, which are placed out of chain position or very axially, and we bind them together by a dihedral potential in this cis position, so any displacement of those, any twisting of those will cause an energy penalty, so and actually the force constant for this interaction determines the torsional stiffness of molecule and we know from the experimental data what should be the value. Now, this construction was very convenient to use also to create a model for our active swivel or the gyrase. In this case, we continuously worried the angle or the period in this interaction, so this introduced, this acted on the other periaxial particles and also this was a model for our gap region. There in the gap region we suppose that there is a segment of DNA where the transcription was not completed and the gap was this, there is only a single stranded DNA so this region bends much more, there is lower bending stiffness and there is also this, it's like simple polymer, so it can axially rotate, so we interrupt this interaction. So this is once again about the gyrase motor, so these are our real beads, what we see in black here, here we have these virtual particles, basically vectors or the particles which don't have excluded volume and so on, but they still have some rotational drag and so this is how we create motor, this is the equation of motor and the speed of motor was calibrated in biological data, which was about 5 rotations per second. Ok, then there are still those immense number of solvent molecules which we treated by replacing them with an integral parameter which was gamma or drag coefficient and we used this Langevin equation, this Langevin dynamics. Well, because we wanted to simulate this supercoiling and so on, for our model it was also important to have the coefficient of rotational diffusion, so we added to this periaxial particles this gamma coefficient as well and we calibrated them with experimental data by playing with the length of those arms and values of those gamas, so we got to the experimental values. Of course, in the living cell the viscosity can be much higher because there are a lot of crowders, a lot of organals and so on, so this environment in the cell can be very visk, so it was important to have a grip on this interaction as well. Ok, so in this way this is the simulation that Lindsey Hiddrich didn't show, so this is to show that how efficiently we can scale up to really tens or hundreds on the scale and going up to our biologically interesting data. So now I'm coming to the simulations, so this is the simplest case, it's an open chain or linear chain but we made a knot in there or crossing and we localized it, we just pulled the knot by simulation to have it here. We put a gy-race, so now we indicate also the initial position or the position of those periaxial bits which store the information about the twist. And now let's start the simulation. And we see that the gy-race starts swivel-ing, it introduces this twist, it transforms it to right and this eventually pushes, it creates a gradient in the open ends of this system and it pushes all the entanglements out from this system, so once again so we can see that really this action of this gy-race can help it to or can direct entanglements to go. Now we would like to see the situation in topological knot or closed knot, so what we did, so we need to have a closed molecule but which is allowed to release the supracoline axially rotate. This is in biology the situation of nicked DNA. So in the place of the nick one of the strands is just interrupted and this is the situation of the simple polymer again which is able to rotate. So now we have again this very simple trefoil knot and we have here the position of gy-race and this is the position of the nick and we start simulating so we introduce the supracoline by active swivel-ing by our gy-race and we see that all the entanglements are all the way around so they are taken towards those nicked regions where the supracoline is released and they are directed by the gradient of the supracoline which was shown. So this was again another situation where we wanted to see what would happen in the case that gy-race and the nick are placed asymmetrically or randomly on the molecule so again we started with the structure which was generated by Monte Carlo of course the molecule was not supracoline so it's really a coiled structure now we started simulations and we see that after some time of struggling and so on again the entanglements were pushed towards the nick. Now we wanted to see also what happens in more complex knots. This is the knot with eight crossings which was not observed biologically but this is actually the advantage of the computer simulation that once we have a working model we can try a hypothesis and see what would happen or predict. So here we have this very complex knot and again we see that upon swiboling the supracoline is introduced and all those entanglements are pushed and localized around the nick perhaps once again. Now what would happen once those entanglements are localized in one place. So as I said in biology we have this closed molecule which can axially rotate it's called a nick but in our case we will consider another case which are gaps and gaps are parts of molecule where the replication or transcription was not finished and there are spaces which were not filled these are so-called azaki fragments and there we have only single strain DNA so it bends a lot in this place it has lower bending stiffness so we put this into our model and we can see that when those crossings are localized and in the position of this nicked part which is actually where is a single stranded DNA where it can release the twist supracoline and when it is when all those entanglements are pushed towards this place and they create a convenient position for bent region g segment which wraps around DNA chain because of its lower stiffness so and as for the topoisomerase now there has been there have been works by Sol and Neumann who created artificially such system where they had this gap DNA and they attached it to magnetic tweezers and they added topoisomerase 3 and they twisted it and they saw that there was a release and there were passages created by this topo 3 and there were also other works which already suggested that there could be some long distance action interplay between gyres and topo 3 so at this point our model was complete so we had this molecule our DNA which was able to keep the information on the twist then we had our active swivel put there also the gap and also we considered the action of topoisomerase and so our modeling process was at the end then we put this into our simulator and we ran the simulation so and this was the case of anoting so this was a knot with the gap region with gyres introducing supercoiling pushing all the entanglements towards the gap region and eventually it made a passage now we wanted to see also that catenated system because the catenates they are created always so as I said they are somehow more interesting so again we had this system of molecules which could be supercoiled with active swivels with gap region in this gap region we removed extruded volume interaction but we kept still the electrostatic so there has to be some work done to make the passage and this work is done somehow by this pushing by this supercoiling here we go both are disentangled so these are the conclusions so we propose the model and we propose the important role for anoting a decatonation so somehow a take away message is that in our mechanism we have the place where the decatonation will occur this is the nick and then the topo comes there and the topo isomerase will wait there till the entanglements comes and makes the passage so it's not the topo isomerase who seeks for the place where it should act ok so I would like to thank for your attention I would like to bring to your attention also the work so the first work is basically what was presented here the second work it's by Eric who will present tomorrow so it deals with the case when those okazaki fragments disappeared they were already filled and topo 4 has to take action and then there is another work which we did in a crowded environment of supracromolecules so it can be also interesting