 Okay, good morning everybody. I think it's quite tough to be the last one so I am always afraid that I don't have anything new to tell you, but I will try to surprise you with something and then in the end you can just complain to the organizer why I am the last one if I am the youngest one But this is the life Okay, so as you probably know Proteins are fundamental ingredient of living organism in order to understand how they can function you need to understand the structure and you need to understand the day dynamics as well you need to understand the links between the structure and the dynamics however, this protein has additional one fascinating feature and more precisely So before I will tell you what is this fascinating feature of this protein I would like to tell you just to remind you that if you would like to understand the function of the protein you need to take care about the primary structure so you need to Yeah, so you need to think about the primary Structure you need to think about the secondary structure and three-dimensional fault of the protein however, if you look on this protein then You can recognize this future is nothing so the nothing is very difficult to see by just visual Expection, but as you know you can just pull the protein and then you can recognize that it's not it So today we know that protein are not only noted they can have a different type of the slipknot So the slipknot is exactly what you have on your shoelaces when you tied your shoelaces They are stable, but you can just untie them by pulling in by the terminal and The second part of my talk will be about the lasso type of the topology that we found Recently, however behind this there is a some basic question that I would like to ask How to characterize entanglement in proteins and what is biological role of entanglement and how noted protein can fault So I think we know a little something about the folding of the protein So I will just refer what we know up to now and then I will concentrate on the some new results They are just published about the function of noted protein So just to remind you as you probably know Protein are synthesized as a linear sequence of the amino acids and then there is a magic trick. They they need to be Fold So it's a question how the protein can be fault and what is important for this talk is to know that all protein They are deposited in the protein data bank because I will just make a few surveys across this data bank Maybe I can just move it a little bit. I can see something so But to discover how protein can Fault and what is the function of noted protein then we need to add this additional future. We need to take care about entanglement So as you all know there there is a not very this is a basic tool To classify the notes but the notes in protein are on the open arc So that's it's something that you can think then other approaches approach of the Alexander grade But it's not maybe the best Because if you just cut your protein like this then the function the protein will lose the function So I what I would like to do to understand the How protein is noted and what is maybe the function of noted protein? I would like to use the let's say All the approach with the cutting the protein and the mother approach of the note story So to understand where the note is located in the protein and see if there is no Other hidden notes in the protein structure. We develop with Ken Millett and Andres Tashak and Eric Redmond some times ago something what we call the matrix model. So the matrix model is the somehow approach of Alexander grade so you have your Protein and what you can do you can just clip some aminus if let's say from the end terminal up to some point When the when I click one more that it will untie it So I can do the same clipping. So this is what you will see for example on the And on the x-axis of this matrix So I am clipping amino acids from one to One seven from two seventy six and then I can see that the note will disappear However, I can do the same kind of the Alexander grade approach I can clip from the from C terminal Toward the N terminal and then I can see that if I will clip in this case Now a few amino acids from C terminal up to some point the note will untie it So in such a very simple approach of Alexander grade you can discover that there is where is the Minimal core of the knotted protein. However, you can Think that maybe clipping just from one side is not enough Then maybe you can would like to clip from both sides in the same time And if you click both from the both sides that you can discover your shoelaces If you would like to know if your shoelaces are properly tied so This is let's assume. This is your shoelaces. It's a kind of the proof that if I will pull let's assume They will untie it However now to see if there is a note what you have to do you have to clip one of this terminal up to some point Let's say if I will clip to this point Wow, that's was hard clipping then you can see there is a note So this is exactly what this matrix is telling you if I will clip a few amino acids from the C terminal So let's say in this case up to that point then you see there is protein is not it So with this very simple matrix model and of course each time I have to close the terminal so the but it's somehow Obvious we close the terminal on the huge sphere then we can see that this We can call That's just jumping okay So those protein that has this kind of the matrix if the corner is full with some color Let's say the green one corresponding to 3 1 we call a noted protein and we call by letter key And this if we have the the corner is empty then it's definitely has to be a slipknot and This we will call the by as a slipknot So with this just to remind you now you can see that protein membrane protein because very complex motive they are composed of 3 1 not what you can see here first of all the corner is empty That's implying that's has to be a slipknot Then you see there is a 4 1 not and then again the 3 1 not so this fingerprint is kind of the topological Fingerprint of complexity of notes inside the protein, but this is somehow So then if you use this method then you can scan all the protein there are the positive in the PDB and what you discover that Some of those proteins of course the first the most complex noted protein is a 6 1 And it's composed of another note of 4 1 and 3 1 There is a group of the protein that it's 5 2 what Sophie was talking about this is you be quitting hydro race However, what is and there's some other protein with the complex motive, but what is fascinating about this? Table it's this is telling you that some protein Coming from different family. They have exactly the same topological fingerprint. This is a group of the protein. They are from membrane They have a slightly different function, but all they Conserve the same topological fingerprint. So now you can ask a basic question. Why so there's a two basic question why we have noted protein and Why we all the protein are not noted as we know from the polymer that everything should just easy note But then you can ask so as we know that only currently 2% of the PDB is noted today So why just 2% So this is kind of the basic question But this table is telling you that some of those they survive this pressure to be eliminated during the evolution if you assume that nothing is difficult so what Where I would like to go with this so you know that you be quitting hydro race. It's a very important protein it was It's responsible for the degradation of the protein and for the discovery of this Beautiful pathway and there was a Nobel Prize Additionally, you probably hear from the Peter will know that this protein is very common in our brain So this is also important. It's responsible for some diseases as well. However, what? we would like to claim that this protein has a 5-2 note and additionally What is the conclusion is that? All members of this family conserve the same topological fingerprint. It's composed of 5 2 3 1 and 2 1 and now what you can have you can have the human East and Flapitarium three different organisms that are separated by a billion years of evolution. However they conserve exactly the same topological fingerprint even though the Sequence similarity is very low. So currently I know even that You can't think so one basic or crucial things about noted protein as already it was discussed It is important to distinguish between the shallow note and deep note So shallow note is something what we call and you probably know already that you have a just thermal fluctuation Enough to untie this protein a deep note is something that you have at least let's say 10 or 20 amino acids from both terminal from Aminid and Carboxon terminal. So what you could claim is that this is a shallow note However, we now currently know there are new protein deposit in the PDB that has this note It's this term in the C terminal. It's up to 25 amino acids So we we have currently deeply noted ubiquitin hydrolyze So this is one Conclusion that maybe they survive for some to not survive in this case to provide some advantage and as we hear yesterday, they are not really The advantage is maybe not to protect protein against the gradation, but there could be something else and additional the same kind of the behavior we see in the membrane protein and In this case what you can see that the sequence similarity. It's really low It's something like 6% so for if you are not familiar with the With the methods to predict the protein So if you have the two C two protein, they have the sequence similarity around 30% in the CASP competition You can just easy predict this protein. So this is kind of the basic Sequence similarity that if you have this sequence, then you can predict another protein However, in the level of 6% is something what we will call the novel prediction So you cannot really predict the protein base another protein based on the template From the protein with the 6% of the similarity and in this case We believe that the note is maybe or slipknot is responsible for Taking together all the scallics. They have to move when the ions are transferred across the the membrane So they have to constantly open and close and the slipknot loop that is more by for one note It's just handing them together so if you would like know something about the noted protein, I think we Managed to buy to build a nice server Knot prot that it's online and it's update each Wednesday. So for example this Wednesday We I found four or five new noted protein So it's the server is supposed to be without the error because there's not more that 30 noted protein Each week so I can just easy scan them and check if they're correct, but if you find there's something wrong Just let me know So then you can we collect or update all the information about the noted protein So you can see there is a tree one. There are left-handed right-handed. There is five two six one There is a small group of the slipknoted protein And this is the topological fingerprint that it's telling you how protein is complex It could be very useful to look for the protein that is deep or Shallow because we also telling you what is the core of noted protein and what is the size of? Terminal and I think really soon. We will have the update version with just non redundant set of the data So each protein is represented in a very easy way of the matrix model that you can see Where is the 41 note and you can see all the detail here and as well around the sequence Additionally, you can see where is a tree one note Yes, that's Somewhere yeah, that is here and then you can as well you can see something on the sequence with the different color And then you can see this on the structure. So this is him so let's just Jump for a few minutes to a different topic a folding of the noted protein and So just to remind you I think we all believe that a Small noted protein as Sophie said can be fault and this problem is somehow we believe solved So we assume that cooperative and increasing degree of nativeness are required for rapid and efficient protein folding Reaction we believe that small global protein are minimally Or minimally frustrated so they free energy landscape looks like a funnel So you assume this this kinetics traps are order of few KT so that's there are not enough to trap the protein in some of those states So the protein can just fault according how big is this from Millis from seconds to milliseconds, let's say However, the question that I would like to ask is What we can say about the noted protein And so how does the linear sequence of the amino acids encoded the three dimensional structure? That is kind of the basic question and we there was a nice talk about the prediction of the noted structure So this is in the same direction how likely the notes are formed if we have just 2% of the PDP that is noted That is kind of the basic question What is the sequence of events that leads a protein from a noted states to the native confirmation? Which contain a note so Already we hear something from Marek Tiaplak about this. So as you probably know it's somehow It's impossible to use implicit solvent simulation just to fold this protein so what we are doing we use the structure based model and I Know that the structure based model is not the best sometimes and we the structure based model is criticized because it's minimally frustrated But it's minimally frustrated from the point of view of energy, but I am not looking on the energy of this protein For me the structure based model is a perfect tool because it's even this tool is showing me that protein are Minimally frustrated from the point of view of energy, but there is a huge frustration due to the topology So I would like to understand this topological frustration So just to remind you this is all paper, but it was Really nice because I don't remember but there was a great talk I think the first day that somebody's was showing that there's and you know that notes can be divided for the twist notes And all other so I believe that all protein there will be fine All notes will be finding the protein that has to be a twist notes for one basic reason to fold all noted protein You have to make use the twist Idea so you have to make a twist Loop that is a native loop and then you have to twist this and then what you have to do to fault the three one note There are two options or you can just go directly like this, but this is kind of the anthropically Not really easy way, but what you can do you can do your shoelaces idea. So you can Do the slip knot and then you can tie the protein. So this is Telling you exactly that You do not make the first of all you do not make the random notes You make to make the to fold the noted protein You have to follow very precise move you have to twist and then what you have you you follow the rather my snare move so you twist and then you track one terminal with the slip knot confirmation across the twisted loop and so this was very nice because even the successful rate of this product of this simulation is 2% is Telling you that you can self-tighten the protein However, of course, there is some other simulation that it's saying that you can use no native interaction and drag the protein to the native state So that's I would like to mention as well so coming back to idea of Twist not so the same way you can to fold the six one protein exactly the successful rate of this folding is even lower but to make a For one what you have to do you have to twist and twist half and then drag one terminal and then you will be fault and in this case of Six one you have to twist one one and then half and then you will go to the native Conformation and this is exactly the same what we observe in the simulation So this was done with the Peter will know this was somehow his idea So just let's move so We cannot fold the Big noted protein, but we can try to fold the smallest one. So the smallest one and it was fought already by few people here So in this case, this is the smallest noted protein and it's possible to use the structure based model So this is the moment that you're dragging the C terminal with the slipknot confirmation but you can create something what we call the free energy landscape and from this free energy landscape you can Assume that the main rate limiting step is to go over this topological Barrier and there are two possible way. However What is the conclusion of this results is that? Structure based model again, it's not perfect But it's allowing you to have a good statistics. So you can sample the data You can create the thermodynamics data, but when you're going across this twisted loop what you have you have a lot of no-native interaction and so there is a basic question if you really sample correctly this Intermediate states where the this no-native Contacts are present J by the repulsive interaction in the structure based model So you can claim that maybe they slow down you and this is the reason why we cannot fold the noted protein so what you can use you can use the all atom explicit solvent simulation and in this case you can Verify two results. So you can use the Anton machine data and run Millisecond simulation and what you can find out you can find out if you will start with this kind of the confirmation that you can indeed Fault noted protein by the sleep note or the pool confirmation So I think this is the way currently only one accessible to prove that noted protein or at least this one can self tight and Just to make story shorter there is the The electrostatics interaction are mostly responsible for this trading And this is the same kind of the native contact that I observe in the in the go model. So I will just maybe Jump I have 20 minutes. Yes Okay, so I would like to go now to the kind of the basic question. What is the function of the noted protein? So this is something what we just publish I think One week ago So to understand the function of noted protein we concentrate on metallotransferases the protein that it's responsible for methylation of tRNA and This is Very crucial because it's not so responsible It says essential for fidelity of protein synthesis and therefore for surviving or of organi So if this reaction will not go the the cell will does die So as you know, there's All metallotransferases are possessing the trefoil note and this trefoil note is exactly Part of the active sites where the ligand can bind However, there's another group of the protein that is called has a rosman fault and in this case It's unnoted. However, the protein has exactly the same function Moreover, if you now will compare this so this is what we will call the orthologous Protein they perform exactly the same function. They're responsible for the methylation of tRNA But one is a noted and it's composed of dimer and is binding the ligand in the band conformation and this is in bacteria and in Human and in is we have unnoted content part that it's a monomer and it's binding the ligand in the open conformation So I think it's a perfect tool to compare. What is the advantage of not if we have two Protein they prefer the same function. So then you can ask question What is the legal why the ligand is bound in the noted protein? Why we have the homoderm why the noted protein is homodomeric when the another one is just monomer and So to solve this Or to learn about the difference between those two protein we combine the experiment with the theoretical results. So we choose Based on the sequence alignment, we choose 15 different amino acids Inside the noted core of the protein outside the noted core and those there are Responsible for tRNA binding and then when you mutate those amino acids, then you can Do the same kind of the mutation in the computers. You can calculate the free energy and you can compare the results with with those from the experiment and what I'm showing you I'm showing you here the experimental results. So we measure three things we measure the Matulation transfer, so how fast the reaction will go we will measure the if the binding tRNA will change and we will measure the binding of ligand and As we expected some amino acid are responsible for the binding for binding tRNA if you mutate them There's a huge difference. However, there is some mutation. They are very surprised So for example this mutation at amino acids 115 because this amino acids is not in direct contact either with the ligand No with tRNA and not really responsible. It shouldn't be responsible for the methylation So, however, what you see here if we mutate this amino acids, they're surprisingly Decrease in methylation process. So this is why we use as well the simulation So now if you use the implicit solvent simulation with all ions and it will be the most realistic simulation that you can perform for 500 Miniseconds 10 different simulation day you can prove they are converging Then you can observe that mutation of this amino acids is destroying the network of hydrogen bonds interaction They are responsible for the methylation process So this implied that the no amino acids in the ligand. They are indirectly Responsible for the transferring the signal the free energy signal from the ligand binding to the tRNA Additionally, you can ask additional question is Why we why not that protein has a Legand in the band conformation and a noted one is binding the ligand in the open conformation And then you can again explain this by the simulation so you can We observe in the simulation as well the open conformation of the Ligan, but in this active site that is not protected by tRNA But when we dug this ligand in the open conformation To the sites with tRNA what you can just easy by eye recognize It's impossible by static crash to have the ligand in the band conformation. So only one possible is a In the straight conformation. So you have to have the ligand in the bound conformation however in the case of the unnoted protein you can have both conformation Just to one more things and why we why we have a knot So then you can use this Ligan to try to so if we know already that the ligand has to be in the noted conformation to assure correct free energy pairing with the With active sites then you can ask why could we have the noted core could be Unnoted so there is one protein that was crystallized in a noted conformation that I think is just mistake But it's a perfect object for me to prove that What's or to check what's will happen if we have the unnoted core? So in this case if you will have unnoted core, it's impossible to relax the structure to bind the ligand, but this ligand bound to Unnoted conformation will be never stable or will be not stabilized by the interaction with the some amino acids. So this is somehow Direct proof that if you will have the unnoted conformation Then indeed you can bind the ligand, but you can only bind the ligand in the straight conformation as a stable Something that it will be stable, but we know from the previous picture that this Straight conformation of the ligand is impossible for binding tRNA. So I will just Would like to mention that one of Idea that I have currently is we know that the ligand in noted Core has to be bound and has to be very stable. So now we can use this idea maybe to to design the selective inhibitor so we know the Metatransferase in human are unnoted one, but in bacteria there are not at one So maybe we can use this ligand that we know that has to be really in the bound conformation we can stabilize this band conformation and then extend this and Create something what it will be the selective inhibitor to block bacteria or material transferase But now I would like to jump to The lasso project. So if you will this is just the Protein with the NNC terminal, but then you can see that some protein as you know They they have the system bridge and if you you make this system bridge, then you can ask the question if there will be Any type of the protein when you will have one of the terminal that will be dragged across this loop and this is Coming back to the I think yesterday talks about the minimal surface. So to detect the lasso protein I'm using idea of minimal surface so We to find out what is the Surface spun it on our covalent loop. We we consider this what I just said this minimal surface And then we analyze the intersection of this Intersection of one of the tape with this surface. So this is let's say the Ideal minimal surface and this is something what we will see in protein and Our algorithm is very simple We determine initial set of vertex and then repeat minimize minimize area around each vertex and minimize area and edge swapping so This is example of tool surface and this is somehow Spun it on the same bound on the same edge And what you can see here. This is slightly bigger than this one So we are looking for the minimal surface that will look like this and this is the superposition on the protein so this is not what we would like to see we would like to see the minimal surface that's looks in such way and so with this method then we can That it's as well the idea of soft bubble we can Scan the PDB and then we can answer the question if there is some other protein they have the last Apology and We found there's at least as you can see 18% of the protein deposit in the PDB from non-redundant set that is Possessing a slipknot topology. So over now. I could ask you How complex can be a lasso protein? So they are quite complex So we have the last so what we will call that we have one day that is dragged across the loop Just once that we call the single lasso we have some protein that you have the this tail is dragged On out. It's similar to the slipknot. So we call this double lasso Sometimes you have the triple lasso However, what it was the most surprising for me that we find something what we call the supercolling So in this case you have one day that is dragged Across the loop and then one on across the loop then it's going back from the other side and back from the other side So I think I call this supercolling. It's I don't know if it's the best name, but it's Something that's remind me and of course we have something what we call the two sides Lasso So this is one of the example of supercolling protein that what I maybe this is why I have in mind to call this supercolling So this is the our protein then you can see where is the system bridge This is our minimal surface that it's spanned on the covalent loop and this is another kind of the Representation to see where we baricentric representation where we see Lasso so all the because it's Impossible to explain you now all the lasso protein and the supercolling and they're really interesting So we make the the server where you can find all lasso protein and I can tell you that the the highest one is we have Protein that you have one day that is dragged at least six times across the loop and the most supercolling protein is with the Three times dragging so the result visualization is similar as in a not for just that you will get to used to So we have the protein and then on the protein you have the minimal surface that is spanned then you can see all the information about the crossing direction of the crossing the size of the tail so to See if it's shallow or deep and everything is well as well as projected on the sequence so just to finish so this is what we Build currently this is our kind of the evolution of topological tree and what is surprise you don't see all the topology here So I don't know this is something that it's still not crystallized because it's just too difficult or the as we know from Sophie there's some on some group of the protein that are crystallized and to make probably to make Protein there are more complex you need to bigger protein and there are a little more difficult, but what you can see here. This is the zero last so then you can have L1 and minus 1 so I use just the Product vector to see if it's from this above the surface or below so we have all the protein with two crossing so you can have double last so you can have A slipknot any as well you can have the super calling However, if you go a level up with the tree crossing the blue one is what we have currently and the gray one is what I did not find In the in the PDP so this is just the accident or this is the evolution I think this is kind of the open question. However, we know that there's other protein. There are More complex like the with the four crossing or even with the seven crossing But what we do not have some special cases so this is definitely the open subject to classified and to really there is a lot of questions that To answer okay, I have five minutes so just to make this So one of the things that I find interesting about also the last so protein and the noted protein most of the noted protein are enzyme but it's exactly opposite in the case of the last the protein last the protein are rather signaling protein or antibacterial protein, but they are not enzyme. However, what you can see here with the single last so it's very characteristics for anti antimicrobial protein and there are also very commonly used for the drugs design and this slipknot Kind of the confirmation is characterized for the signaling protein I do not have currently proof if this is the topology that is Deciding about function, but this is I think something to explore Okay, so there is a different type of the amino acid that you can close and one of the most common exam that it was found Definitely before our discovery and this is why I call this last so noted the tadpole as the suit I was calling because this is very old protein that it's Used to block polymerase that you have one day that is crossing across the surface and then you have two bulky amino acids They're blocking this. So this is kind of the historical reason why I'm using the lasso name not the tadpole Name so maybe I will just skip the Other function, but now I would like to ask you a final question Do we have links in protein and there is one nice paper that I recently learned as well about the links So it's was done independently So our definition of the last so is we if we think about the links in the protein Then we can distinguish between two type of the links. We can have the deterministic links that will be close by In this case by the system bridge So you can have one single protein chain and on this one single protein chain. You can have two System bridge, however the loop in this case will be crossed by the another loop So this is what I will call deterministic slings. This is another example of the deterministic slings made by two chain but independently they are close each other and this is the approximation of the Probabilistic slings so we have two chain, but we will close them independently So to to find out if protein has links I will use as previous the idea of the minimal surface So this is kind of the representation of the protein with the n-terminal c-terminal and in this case We can have the classification based on the corollity and orientation because we have both the orientation of the loop And we know how the one loop is passing across another one And then we can span the minimal surface on one loop and then see if the surface is crossed by another loop So so this is our minimal surface and this is the results. So currently in the PDB This is the links that deterministic slings So we have the hopf deterministic things that is one of the It's I choose this protein because it's the smallest one So it's very nicely packed and it's very beautiful and then almost by eyes you can see the hopf link There's slightly other bigger protein as well with the hopf link Currently, we know that the single protein chain can make also the Salomon link and We have the Boramian ring so something that I think definitely needs to be explored more and But what it has to be explored more because it's not really easy to determine this So this is the simple example of the link However, if you will have such structure that you have one loop that is dragged by across another one But there's some other loops or in this case that something is additionally twisting That's something probably what I need more help from rotation or as well here This is very nice exam that they can be quite complex. So just to finish Something what I find very interesting that as in the last protein it was difficult to assign one Function in the case of the link There is a unique correlation between the Salomon links and exactly the same biological function So that's something that there's no or maybe there's not enough protein But all Salomon links as are exactly adhesive protein So to determine the probabilistic slings we close the two terminus of the protein on the sphere There's a different method what I learned Two days ago from our landing paper So it will be very good to compare this so currently you can just go online because I cannot talk about all of those But we have online server that we call as well the link plot where you can find all the information about the Both type of the links deterministic and probabilistic. So this is the current classification This is deterministic slings. However, in the case of the probabilistic slings we make an additional slider. So this slider Okay, so there's if Sophie cannot see because So in the case of the probabilistic links you determine the probability which you will have Type of link. So because we don't know what is the what to say If it's 60% of the probability that this will be linked or maybe 50 So then you can rather just decide by yourself. I would like to see all the links in Protein they have at least 10% of the probability To exist or I would like to see the links that you have at least 80% of the probability to exist So this slider will change all this table and we currently go up to four Change so that's zero minute Okay, I am finishing and I I think it's necessary to say that this server and was built with the Crucial help of Ken millet and Eric Radvan I will be not able to classify all the slings without they help. So and as before Now you can have minima surface. This is HV protein that you can see that it's linked and I think it's the same As in oil and any paper, but then you can have all this Interactive cycle that it's telling you what is the probability that you will see the the hop fling unlink and all other So we go up to 1% of the probability So I will just finish with the something what I am working currently now I would like to classify the macro links So this is the virus as you hear about before that the DNA RNA is bugs But you could ask the question why the virus is so stable And I believe it's so stable because there is links inside They are stabilized this structure and the highest link what I found I call the flower link So this is something to explore. So just to finish there's a lot of application And this is I think the most complex noted sleep noted linking protein in the PDB and I will just finish not to stress Eric so The function about noted protein is work what it was done with my PhD student with Agata Perlisca Alexandra is responsible for most of the server and she's amazing Pavel is classifying all the notes and he's also amazing and Vanda is the first person that I start to collaborate after my postdoc, so this is my group and all my collaboration and I have Some source of the man is so I am looking for a good postdoc or PhD if somebody will be interesting. Thank you