 So, thanks to the organizers, first of all, and the judges for giving me the chance to talk about some of my work that I've been doing during my PhD. This is a side project, so I made a project when I was doing this stuff when I had some time and not doing making pasta, so when I was not making pasta, I was doing this. So, starting with this picture, which is the same picture that Randy Cummins showed in his talk, and this picture shows it was taken in the 1970s, and it's the Kinetoplast DNA, so outside is a natural environment, which is the mitochondrion of some organisms of the class Kinetoplastida, and what's peculiar about this structure is that it's fairly unique in nature, so these are all small rings, there are links together, and they are all packed inside this disc-like object, membrane, in the mitochondrion, and when they are taken out of from there, they look like that, so they're all linked together. So, in the 1990s, the group of Cossarelli started to think about this problem from a more mathematical and topological point of view, and they suggested that maybe this network is made of, like, you can think about this network as a two-dimensional layer, where you have rings linked together in this fashion, and you can check that by doing digestion experiments, so you put the restriction enzymes in the solution, you break down the network and you see the products, and you can check whether your model fits the data, and I don't need to tell you that this structure really reminds Olympic gels that were imagined by the gents, and as far as I know, no one has made an Olympic gel, a synthetic Olympic gel in the lab up to now, but nature has been doing it for thousands and thousands of years, so maybe we can learn from nature, also in this case, try to make something smarter. So, I started from that picture, so my work was motivated by the fact that the Kinetoplast seems to be biologically successful, but how can we understand that? I mean, can we understand something better, more destruction? So, what I know from that picture is that the DNA is all packed under strong confinement in that disk shape object, and so what these people have been doing, some of them are in the audience, actually, so it was to model the network as two-dimensional layers where rings were allowed to link with one another. What I did was to relax this assumption and to simply model, do some brand dynamic simulations of rings that were allowed to pass through one another, and then from there you freeze the network at some point, you compute the pairwise linking number, you get the network out of that, and from the network you can compute whatever you like, for instance, you can compute the mean balance of the network, that probably the distribution of the linking number, and then what you can do, you can simulate, you can do the simulations of this restriction, digesting experiments, and you can do it for different system densities, and then you see that this value of density and the products that you get, the relative abundance of the products, they match pretty well the data from the Kostarelli group, so then we went back and then said, well, what about that density, what's special about it, and then we discovered that density corresponds to this point in this graph which shows the size of the largest connected component in the network, so what it means is that it's surprising that it's not either down there or down up here, it's right bang in the middle where the percolation is start to take place, so what we argued is that the network is near the percolation point, and then you can imagine the kinetoplast as being optimizing the linkedness of the network, so it's neither, and this is biologically important because clearly you want to keep all the genetic material together when you divide, but then you also want to do the replication quite quickly, so you don't want to unlink, you don't want to be super linked because otherwise you'll have to do too many operations, and so I don't have time to go through this part of the talk, okay, so a very cool experiment that I want to just to mention briefly is this one, which is so how the replication, so even Kamin was saying how does the replication occur, because if they are all linked when they divide, so the point is that basically the network seems to rotate around two fixed points, and then the mini circles get unlinked from the network, and then re-linked at the periphery of the network, and you see here the tagged newly produced mini circles that are introduced from the periphery, and they diffuse inside the network, that was pretty cool I thought, and we tried to come up with some simple model, and we are working on it, and here I end up thanking collaborators and people having the honor to talk to Ingorek, Gareth, and Tom, and Matthew, I remember so, and Edinburgh, Fundings, HIP, PSSC, and this is some linked pasta, I want to do the whole Kinetoplast, so then I go quite lazy and I stopped at two, so. Okay, time for a quick question, I've got one, the Kinetoplast network has maxi circles in it too, did you put any of those in? No, they are biologically important, that is for sure, but we haven't taken them into account in the model. Okay, well thank you. Ah, that's a good question, we haven't checked the distribution, I haven't checked the distribution, I don't seem to have, but the average variance in history, this is a good point, I should look at it. Okay, let's thank our speaker again, the next talk is by Wandan in Piscaya from Warsaw, talking about complex lasso topology in proteins. Okay, good morning, I feel very honored and quite surprised to find myself on that side of the audience today, I'm a mathematician who work with some theoretical staff, functional equations, and so on, and I was very lucky three years ago to meet Joanna Słukowska, and because of her to meet all of your society, work with Ken, collaborate with Eric and with the others, and to get to know a little bit of your beautiful and colorful science, I'm very grateful for that today. And this is my poster, which is kind of a picture of last two years of my life, of my adventure with Joanna, which resulted in those free databases and servers on the complex topology in proteins, so Joanna showed all of them in the morning today, I will try briefly to encourage you to use them. So, not protein is the first one, which collects all the information about the nuts in the proteins, so all the statistics from whole PDB and the detailed information about each particular structure, and what's the most important, we also have a server for you where you can upload any structure, actually it doesn't have to be protein structure, and you can get all the information, and in case of any questions or any problems with the user server, please contact me, and then the second one is lasso abroad, and Joanna told you a little bit about lasso, so lasso appearing in the protein when we have, in any structure, when we have some additional bond that creates closed loop, so we have closed loop, and then the tail can go through the loop, can go, can go around or can do whatever it wants, so those are the lasso types that we have found in proteins in the PDB, and in this case we also have a server for you, for instance you can upload the trajectory, you can choose some options, more detailed or less detailed calculations and many other options, some advanced options, and in the case of trajectory you can get such results, so there is no time to explain you in the details, but I just want you to make me believe that from this picture you can very easily see that in this case we had some loop, and the tail went through the loop first crossing the loop in two places, and those two lines show us that there were two places, and then it went totally through the loop, so anyway you can really see from those information the pattern of folding the protein, and you can also see the detailed information about any frame, any structure, and also in any question, in the case of any questions, problems, this can take me, and then the last one, link prot, is from this summer, it's very very very fresh and very tasty, hopeful, so for two chains, two open chains, we close them on the on the spur, so we obtain few link types for any structure with some probabilities, and what kind of links we have found in proteins, we were looking for the links between up to four chains, so with the probability higher than 50%, we found two links for two components, only for two components, hopp and solomon, for the probability 30%, we found star of David as well, and two links between three components, and for the probability 10%, we found a couple more, that one is the most complicated for two components, has 10 crossings, and as I told we checked also all the set of all four, all the sets of four components for chains, and those are link types that we found in proteins, with the probability higher than 10%, and this part of our project was kind of exciting, because those structures, they aren't in any tables, link tables, not tables, as far as I know, so that was kind of exploring, kind of exploring new things, okay, and here we also have server for you, and in case of any questions and problems, please contact me, those servers and databases are made for you, and I hope that we can together move on with some new discoveries with those other things, thank you. Okay, quick questions. Well, I'm going to stop by, I think my question's unfair. I'm just, I want you to speculate about, kind of looking forward about our ability to design knots, any knots, with protein chains in general, knowing what we do about all of this, how easy, hard, what do you think the challenges might be? Perhaps that's unfair. So if you're really interested in my opinion about that, yes, you know, I'm not a specialist in those, in this thing what you asked about, but what is exciting for me with that collaboration, that they really, what I can see here, I really believe that those things are possible, and that's what I, I think that the thing that you asked, it's not easy, but I hope I will see in my life then, yeah. Okay, let's thank our speaker once again. Our next talk is by Antonio Sumo from CISA in Triesta, poor translocation of knotted chains. I would like to thank the organizer for choosing my poster. I'm going to talk about my work during my during my PhD under supervision of Christian, which is on Portland's location knotted chains. So the motivation of our work is the ongoing effort to sequence DNA. In this case, sequence single strand DNA making them pass through nanopore. This sequencing experiment are involving longer and longer chain, which have high probability of knotting. So we asked ourselves what can be the impact of the presence of knot inside the chain when it starts to translocate. So our model is a really a basic flexible chain, which is mapped on the single strand DNA, but can be regarded as a zero model for other biopolymers like proteins because you have some charge interaction, but it's really screened. So the first work was done by our group in 2012 and shows that microscopic intuition or friction is how different practical one. So I'll tell you the translocation is going to follow. So the tension from reach the pore that is located here in this case in the green region, then the knot tightens and drags toward the pore and here it gets stuck because we choose a pore small enough to make all the single strand pass. So while our intuition phase, you can see that in the case of low forces, when they're not reached the pore, the translocation can still continue to go on until the end. While for high forces, this is not the case. As you can see, it gets stuck. So we let's say recover our intuition. So we started from this observation, let's say this phenomena and try to understand better, which is the impact of the other different topologies, most simple one, let's say, and even some composite knot. Here is the basic phenomenology. So you have the velocity to translocate 30% of the chain for different topologies and different color representing increasing force. So in that not that case, yeah, that when you increase the force, the velocity is just proportional. Well, if you, let's say, select here, twist knot, you have what I showed before. So for small forces, the translocation can go on. Like for high forces, it jumps. This is the case for our twist knot. Instead, if you look at the twist knot, the situation is different. So yeah, the translocation can go on. Anyway, for these cases, you can see that the scale of the velocity is different from the, they're not the one. So in any case, we have some impact in translocation. Another nice feature is that if you have composite knot and change the order in which they arrive toward the pole, you have that the velocity is different, as you can see. So if you want a better explanation, you can come later to my poster in the last minute. Here, I'll tell you briefly how we characterize this phenomenology. So in particular, we measure the tractive force before and past the knot, because you can see the knot as a dissipative machine, for which an applied force, an output force, which is a smaller one, we measure this output versus input force, and you can see that for the twist knot, you have the force decreased to zero, where for torus knot, it continues to increase. So basically, the difference between torus and twist knot is that torus knot have just one single tracking points, while twist knot have at least two main tracking points, one at the entrance and one at the end, meaning that the friction is different. This plot also can let you understand where composite knot be in a different way if you change the order. So you can see composite knot as the sum of sample knot, in which cases you can compute this force before the second knot using this diagram. So actually, changing the order means that you compose these curves in different ways, meaning that of course you're going to have different results. And this concludes my presentation. Thank you. Okay, time for a quick question or two. Nice talk, thanks. Maybe I just missed it, but I didn't understand how you applied the force. Okay, yeah, no, I didn't tell you because it was too short. So the force is applied just inside the pore, as done in experiment. So it just applied, let's say, an electric field inside, and it starts to translocate. So does every bead fill a force or just one bead is the force transmitted along the chain? No, no, no. Okay, the force is applied just inside the pore, but of course it transmits along the chain. There's a lot of paper solution on this. So yeah, the force is transmitted toward the end of the chain where we're doing it. It started to rectify during it. Great. Thanks. One more question. Let's thank our speakers again. On behalf of the organizers, there's some very special people we'd like to thank. One is our technician, Iqbal. So give him a hand. But a very, very special thanks for our secretary, Erika Sanataro. Erika, you've done a great job. And on the behalf of the organizers, thank you for coming. This was a terrific conference, and you made it happen. So thank you.