 Dobro. Čekaj za to, da me počekajte. V toj veliki venič. To je menej prvič, na kratku CTP, ali sem odložila toh, da sem odložila menej studičnih vfizikov. Včasno, to je veliko odložilo, da se pravimo, da se počekajte, in da se počekajte. Speciali v različnih različnih različnih različnih različnih različnih različnih, In tega je vzačno, da vržite vsi, očeča, da je nekaj našličj, vzelo, da je nekaj našličj in odličujem, da so do vzelo. A Slovenstvo vo vzelo po bližji v Vienni, in tudi prav se zvisno tato, da se vse uč hara pre grozizaj za drugičil. in zelo vzaj delaj je, da nečešel si je odstradil do več nekaj odstradil in do nekaj nekaj odstradil v particučnih, da je se učaj da je vsega ojda. Tukaj, pripovrste, da je tvoja je svoja tjera, da smo povoljati v Vienna, Vsih šežem kaj smo početili, da se prišli vse nekaj obpolj, dobro jaz mu je však z delih nještih, zato pa vse ga jaz navetimo v početnih za proč, ko je počet, da se početimo. Čutvo, da bo, da vse prišli, da sem da se početi, da mi ampak vse, da početimo, da si početimo, sa vsev stranbeni. Sojwerk je zovem, da zareštimo tako slurje, nekaj leži, nekaj ležimo, in otvarimo v zaštih aplikacijs z nekaj nekaj nekaj pošljano do vene, na kaj je zemljačne vizivizve. Danes jeega aplikacija da je dobročena, kaj je ojduči drugojevim čežovim, in izgleda stabilitve biomolekulje in izgleda tega topologičnja stavlja. Zato, da je tudi nekaj izgled, je tudi venom z vsej zelo, da je vsej zelo izgleda, da je več effektiv, in vsej, da je vsej zelo, da je vsej vsej zelo, da je vsej zelo, tudi na zapečenju, že si spliti tukaj, naše zelo glasbo tako, raztukaj zelo, ta zelo mi se finativa, je zelo prič zelo, ki je što veseljne, ki je počutka, ne musi se na gorovav več, da ni se tako ne ste. Telo mu je nibs začelim, trenu ki je v axisera enk Cock, počutku počutku, je nešto, ni se nešto, ni se nešto, ko je proj stays, sweep, delivery and material science. What I would like to show you is the question of how can you design級 to do what we are doing in this movie to reliably fold in to a very specified note that you want a peohori given, okay? In other words, we want to ask a question that is across the domain of Polymer Physics and prote any virtue. v protiči, to je izgleda razlika rezečna, o kaj smo svačili v Vienniji. Kaj smo počeli, da smo nekaj zelo počeli, nažal jistimo, nažal še nekaj zelo počeli. Svar, da so svoje protiči, je nekaj izgleda nekaj izgled, da je kaj, da vse potrebevaj vstaj, tako, še nekaj kaj je začilo, nekaj presez freezing. Svar, da so se tako, from this system and then apply here, to be able to ctrl the structure, and then the nothing properties. And so this brings us to the idea I would like to give you certain, a little set of definitions first of all what we mean by design, so design is the process that you have to apply in order to search a sequence of letters in the case of a protein will be a sequence of a minimize in vseh, da je pošta, je semadni z vseh, bo imaš neko vseh, ki je sveti, in zelo v loži, ki izgledaj, nekaj neba in unik nekaj struktur, ale vsak vseh mali in nekaj konfiguracij, nekaj je vseh z vseh, na poslednji proces. Vseh, da se bom vseh sezipel, a zelo bi sezipel nekaj soličen po vseh. Tako početnja, premače, da boš početnja, je, da se pravdješ, da se obžitele in vse, kako se zvukajite, in ne najteško prejšel, tko da se zelo začel, doblikaj se, da se však ne početne v tukaj začetne in tukaj se doblikaj, da se zelo začetne, pa doblikaj se o dve, početne vse začetne, Algoritm je veliko komplek, ki so prišli. Musim se početiti, da, od systemu, kaj je tudi taj proces, početiti jednodimensionalne informacije in sequence in tudi tudi tudi tudi tudi dimensionalne informacije. Protojnje, da je. Protojnje, ki so početite, je, da, če je protojnje desajne? To je vsebe, da je vsebe, kaj je protojnje početite, če je to jedno prezvom vzgične zelo, ali se je vzgleda vzgleda, ker je izgleda tako, da je tudi drugi našličen, da je to, da je evočen, da je to zelo informacij. Vzgledanje, da so... Mi se poživite, ni tudi nas vzgleda, protimizeri, posunje, tudi nekaj vzgledaj 20 nekaj, neč vzgledaj, nekaj ima zelo, in je vzgledaj vzgleda, In sežka na vsečenih prikratov, ki je početno poslednje in začetniti početne konfiguracije, tako kaj smo videli v pravih doma. V obči, da vam se pokazal, prijev, na kaj smo vtešnji postavili v težkiji vseče, je to, da imajš da odstaj taj kustv, na težkiji v četniči zapotili proteinelj. En tako, da je način, da je tukaj, da priča prorabnje protins izgleda idrogyne boče, da je odvijeli do zrponem, da energijne stabilizuje toj struko, hlice in vetneče, je zelo včin, da je informacija in vse informacije. In njegovosno, da površajte model, in se je inšlje inčen površa, se repraviti sequensi, ko je pripravljivni struko po hršenih protins in. In, nekaj ne bi se počutil, da so načinati, da, da se prišli, da sem načinati, in, da se vsega, da, kaj se vsega, tukaj, zelo vsega model in je vsega vsega, protin sequensi, vsega vsega vsega vsega, preseženja na način struktur. Tukaj, ki se prišli, da, ki prišli, da, kaj se vsega vsega, in da se vsega vsega, protin nečine, vsega vsega vsega vsega, proradnje proradnje, pri proradnji proradnji in proradnji vkrati. Proradnja je, da je zelo, da se izgleda, da je zelo, da je tudi zelo, da se je zelo, da je tudi vsega. To je vsega biomimetica, ki sem vsega. Vsledaj, da se zelo, da je zelo, da je zelo, da je zelo, in to bo vse zrpunjati za informacijne konveršenje. In povrdujamo to do povrdu, da je vse zrpunjatega vse, kaj je vse zrpunjatega vzpešnje in tračenje, pače, ki so vse vse vse vse zrpunjati, tako da je vse vse vse zrpunjatega, ker je vse vse vse vse zrpunjati, zato je zrpunjatega in tračenje. In kaj je vse vse vse vse vse vse vse zrpunjate, to pače se zrpunjatega in tračenje. And I will show you that this is enough to actually create designable strings, not touch polymers with very high precision on the target structure. Again, so now I am going to talk about artificial proteins first very briefly, because this is where we started and it tells you how in a way you can construct a system that self-fold into a given structure. So the approach we are going to follow is very quickly on a multi-scale idea. Zato smo smo izvajati, kako izvajati vseh štih predtahvih vrštih, v latičnih protišnjih, ki se učili vživati, ki je tko v HP modelu, in ki se po vštih ledrži, smo izvajati vstahvih od 20 ledrži in zanimamo, ki smo izvajati, da se izvajati, in da se izvajati v latičnih, in ki se površtih, da se površtih, je, da smo izvajati, da smo izvajati, da se površtih, da se izvajati, da se izvajati, da se izvajati, about that today. So the first step to understand, the most simple way to understand protein design is to use very old model called the random energy model that was developed in 1980s by Derrida and was applied successfully to understand the thermodynamics of protein folding in the late 80s, beginning in the 90s by There are several very famous scientists from Peter Waliness, Eugene Shaynovich, Gultin, Panther, Grossberg. I mean, there is a huge list of people that apply the original in the 80s and 90s at this model to explain protein folding. The idea is quite simple in a pinch... The idea will be that if you want to construct a sequence of amino acids that falls into a structure, ...ban potrebno ima izgleda svoj hodny izgled... ...in zelo v zelo vsega je jazem. Vse zelo so potrebno, da je to možno, da če je zelo... ...zelo je dobro svih bojkov, da to je... ...kega pravdu, da vse zelo... ...zelo je sve zelo... ...in zelo je zelo, da je sem vsega. Vse zelo je svega, da je zelo... ...zelo je zelo. zjela. Čestnojo, ki sem tukaj pritvačen, da ga ta pošli vznikovati envoy je to barko. Zdaj je tukaj trgaj, da drugi metr, kaj ne čumblevači zvoljite, je tukaj tukaj trgaj, je tukaj pritvač, neč neč je vendet, je menej, and of your polymer. This is for instance why it's hard to design something with just two letters like the HP model, but if you use three, four, five letters then it's much, much simpler. So this is basically the prediction of the theory. If a system to be designable, you have at least to satisfy this condition. So what we did, of course, if a system is designable, then the design principle is quite easy. Si priključiti to, vsaj se tačnega zrteva, in if this is the energy of your protein, then you can split the contribution in two contributions. If i, j and j are two amino acid pairs, then si i, j here indicates, it's a matrix that tells you if amino acid i and amino acid j are interacting. S i, j is another matrix that tells you what type of interaction there is between i and j. To je matrič, ki teči, kaj je konfiguracija, ker je spesijačnja konekšnja v objevku, kaj sij, ki teči, kaj je natručnja kremijka in trakčnja. To je tudi sekunce, kaj je konfiguracija, kaj je in trakčnja. Značno, je, da se vse zelo, zelo, da je trakčnja, in tudi sečen spas, kaj je minimizirati energij. Kaj je vsečen, kaj je vsečen vsečen vsečen, In potem je težko nekaj našlično zelo, da je nekaj našlično zelo, in v prinsibu, težko je dve ljene izgleda v samih počke, kjer je protein všlično všlično vsega tragetost. Tudi na lati je protein, to je semplno, da je zelo, je zelo, ki je potrebno počki. In počke je, da nekaj, da je začel težko, ker počnebaš to v ampak aradno protein, zelo prezrastová protein-modelški, če so, nek je to nepočasnice so vzupi samih neание, provkaz ne neče ne拜拜 shouldnov? As brz stršno. Frid bude, nek je nene nešte reprezentatične protini preč vseč del vseč, vseč ek😄, ker vočite konfiguracionaln instropija vsih polima se počav tko vseč that this minimization process fails. So basically what happens is that your omega becomes so much larger that with 20 letters it doesn't work anymore. One solution could be to increase the number of letters that you use. For instance, this is equivalent to use the native energy term in the Hamiltonian, which was mentioned in the talk before. The idea is that you include information about your target configuration for the folding. This is effectively like bringing your alphabet to a much larger size because you are saying that amino acid i can only interact with amino acid j and not with the other. So effectively it's like bringing your alphabet from 20 letters to n letters. So this is why you recover your folding. But the other way to do it is to actually try to represent your protein, including the correct set of interactions so that omega is correctly smaller than q, so that with 20 letters this process works again. So we did that in this model, that I don't want to talk about too much because this is not the scope of this talk, but I want to mention it because it's the reference for our biomimetic system. And the idea was to just take a protein backbone without the side chain, because amino acid is represented by this large sphere here, so it's a very simple representation, but you have 20 different spheres represented in different amino acid and you have an interaction matrix that gives you the chemical flavor of each different interaction. And the idea was that instead of trying to parameterize the model to make this object reproduce the folding property of a specific protein, we wanted to reproduce the designability of the model. So our idea was to fine tune the parameter until the omega was smaller than q, so we could actually design this system to fold real protein structure. So we parameterize in this way. If you're curious about it, I will be happy to show you more details about how the model works, but I just want to show you the main result, the fact that it works on the design part. So if we take a series of protein structure, here there are just four examples, straight from the protein data bank, you completely strip the sequence information. Now, this is just the position of atoms in space, but each amino acid now we reconstructed from scratch using the same design procedure that works on lattice protein, and the random energy model explained us why it should work. Then you produce an artificial sequence that might even not be a real protein sequence at this stage, but it refolds to the target structure with remarkable precision considering how simple the model is. So in other words, these results indicated at least our model respects the concept of designability defined in the random energy model. And it's also nice because it gives you a link between the very simple lattice models all the way to of lattice and realistic protein structures. So, again now we want to learn from the protein side and go back to the material science and try to extract this principle and bring it to a completely artificial system that doesn't anymore remember anything on the biological part except on the fact that we learned from proteins how to design a heterogeneous polymer. So, these are what we call the bionic proteins and what we did with it was to represent basically still keep an isotropic interaction as mimicking our alphabet of letters with particles with different chemical properties and we decorated now every particle with this directional interaction that are reminiscent of the hydrogen bonds network on the protein backbone. And so this is an example of the interactions we used in principle this is just one set of interaction but one can think about many others and I will mention few others as a matter of fact. So, the interactions between the center of the sphere is given by this simple sig model function which is basically represented a continuous version of a square well potential and the depth of the well gives you the different type of interactions between the different type of particle you use while the interactions between the patches is the same as we used for the hydrogen bond network in the proteins. So, it's a Lenard-Jones 1012 very sharp of course we can also control the range of it but we started with the same interaction as in the proteins and the Lenard-Jones is modulated by this function of these two angles. So, basically this potential is at the minimum when the two patches look at each other and when they are orthogonal this potential is zero. So, immediately you can actually spot a similarity to what Mark showed this morning on the dipole, the stockmeyer fluid. The idea is that you have an isotropic interaction that will compete with the directional interaction in terms of packing and configuration of the system and so we can actually change the relative strength between these two interactions and the relative range. And so, to give a parallel to what I was saying before basically if you have the hydrogen bonds you basically restrict this configurational space enough to allow designability for the patches is the same thing if you don't have patches you are basically like a simple self-avojding walk polymer so you cannot design it but if you add the patches you restrict the configurational space to the point that you have designability again. But again in the other limit you would expect that if you put too many patches on the system again you go back to the isotropic particle with no patches whatsoever so there will be a region in the number of patches in geometry where the system is designable. So, the other thing so the first thing we did was to try out what happens when you change the parameters so for instance if you take the situation where you have one patch per particle and you increase the interaction range between the particle from basically very short range to long range you get that the system first just is happy in this configuration and then suddenly wants to pack more and more and here you start to see that you have wrapping configurations which is exactly the same as Marko observed in the dipolar sphere system and in fact this one will be what I will show you later precursor of many not configuration that you can design specifically or if you have two patches instead per particle you have a different configurational space and these are the typical configuration the system will adopt. So, the first thing we have to do is define the designability of the system this is what I mentioned before how do we say which patch configuration and range is designable from one that is not designable because in principle what we have to do is to define if there is at least one solution to the design problem so what we did was to make a large scale simulation where we change both at the same time the configuration of 50 of a polymer of length 50 and also its sequence ok, so we basically explore at the same time the sequence and the configurational space and we projected over these two order parameter the probability of observing the configuration in the system so q is the number of contacts between the isotropic interaction so it tells you how compact the object is and qh is the number of patch-patch interaction so what you see is that there is a region here the dark region that is much more probable than the rest what this tells you is that not only that there are more configurations that have this pair of values but is also that there are more sequences that like to be in that region so this means that this configuration that are in the low and the free energy minimum are also the most designable one so these tools is able to it's a tool to compare so different system are designable sorry, different configuration are designable but is also a way to identify in principle the most designable configuration in a given geometry of patches interaction range and etc so once you have this configuration then you can test if it's indeed possible to design and make it fold to a very specific configuration and if it's not then you know that this particular set of interaction that you choose are not designable so you can build up a phase space of it so the first step is to test if for instance this object folds or not is designable and it folds so you select the configuration that is here and this is the case and since I will show you several of these plots is useful to just give it a metaphor we call this the Sauron plot because it gives this very sharp long dark area so this is basically the eye of Sauron that maybe some of you have seen the Lord of the Rings so if you take the configuration I showed you before and you design it as the same way as I showed you for the proteins and for the lattice protein before you can construct a sequence of a amino acid here we used 20 amino acids that will basically fold exactly to the target configuration so this free energy landscape here is a projection of all the configuration of the polymer over this collective variable called the DRMSD which is a measure of the distance with respect to the target configuration so zero means that your instantaneous configuration is exactly equal to the target larger the number more differences there are so basically when the system is so close to zero it means that the system predominantly wants to be exactly in the folded configuration and in fact you can actually use this system to even create very precise patterning so for material science this would be very useful because we have a controlled precision over the structure which is basically about 10% of the particle size and this is something that basically is a precision that proteins have and is the kind of precision you would need to achieve for instance catalytic reaction control over catalytic reaction or structural control if you want to use as building blocks for hierarchical self assembly so as I said with the designability measure that I gave you before then we can compare how designable different geometry of patches so in this way we can actually construct a map of how different patchy polymers are designable compared to the others and basically what we found out is that without patches no system is designable no matter even if you use 20 letters as soon as you start to increase the number of patches with high number of a larger alphabet you start to have designable systems and then basically you have a nice sweet spot between 3 and at least 10 patches per particle where between 3 and 20 letters you can easily design your target configuration to reliably fall to the target structure with the precision I showed you before and as I said also if you increase too much number of patches then this ability is going to go down again because effectively what is going on is that omega so the configuration entropy of your chain is going to start to increase and since the problem to do this analysis is that it is very very difficult to compute omega so in principle to repeat this approach for a different model or a different system you would have to redo this entire procedure of designability and folding etc so we came up basically we wanted to give a quantification of this omega that we could basically transfer to a different system so what it turns out that the best way to actually measure how the configurational space of the polymer was restricted was by looking at the radius of the radial distribution function between the particles along the chain so the geo bar what happens is that you start to have more and more effect of the patches not more and more patch interactions because in all the structure I showed you before all the patches were fully were fully bonded but the patches will start to have an effect over the random packing that you get when you just have a chain of a tractive sphere that collapse into a random globule when you have patches this creates a perturbation in the geometry because also the patches wants to be satisfied and this since they have such directional geometry like the hydrogen bonds in the protein this creates the disruption of the simple random packing and a peak arises exactly in correspondence of the distance the bond bond distance between the patches when this peak becomes dominant in the geo bar distribution then the system is designable so this is a measure that is independent of our model because this is basically what we are saying is that if you have somehow a way to restrict the configurational space with some sort of interaction perturbing the normal random packing of your polymer then your system is a very good candidate for being designable as a matter of fact in fact not only this is true for the patchy polymer but if you go back in proteins and you look at the geo bar in c alpha atoms you get exactly the same kind of peaks that are completely due to the hydrogen bonds interaction and these dominate the geo bar distribution and we are also trying to apply this to different other protein models or other systems that have been candidates for designability for instance the tube model development Maritan Banavar, Micheletti etc. I mean there are many people involved in the tube model and this could be another place to test for instance this criteria but there are several other examples and in fact I would like to call upon Mark if he wants to collaborate on testing this principle on the stockmyre system to see if in fact the dipoles themselves are capable of restricting the directional space exactly as our patch interaction do so and now we go to the core part of what I promised how to design knots so as I said we have a tool now to analyze how given system and to categorize how designable different configurations are but the problem of the analysis I showed you before is that it requires quite heavy free energy calculations because you have to sample the configuration space of the chain quite heavily and we rely on bias techniques that need to have a good order parameter to have the system to sample around so in principle one could think that the simplest approach would be to use one of the many algorithms developed to analyze the topological properties of your chain to assess if you have a knot or not and what type of knot you have but the thing is that most of these methods are even if they are very efficient they are too heavy to be used at every single Monte Carlo step where you would have to assess topological state of your chain and use that to bias your simulation but instead what we did was to implement a method based on the average crossing number which of course doesn't give you exactly definition of the topological state of the chain but what it was found is that it correlates a lot with the complexity of the knot so higher is the average crossing number, higher is gonna be the complexity of your knot it doesn't guarantee you that you will have a knot but at least it will force the system to explore more and more complex places and so this is the basically the plot that you get if you do the simulation of one of the system I showed you before and you force it to explore different chains with different average crossing number and different end-to-end distance so this is still preliminary results we are studying a lot of it and so we are actually curious about if this jumping has any meaning and what what kind of knots we get in this landscape still this is quite an unknown landscape to us in terms of what configuration we get because we still have to analyze a lot of this data this is thousands and thousands of configurations but if you zoom in close to the global minimum you get what we refer what we can expect to be the most designable knot for that particular geometry of the chain and then you can in fact place back this knot in the sovereign plot and you find out that in fact this one corresponds also close to the global minimum that as we know are the most designable configurations of this particular system so we expect these systems this approach to actually be able to sample knots and categorize them afterwards to how designable they are and it will give us also a way to explore different good target good knots to be designed also for applications so for instance if you use three patches and three letters you get the knots that I showed you before so this was the example I showed you was just using sorry here I made a mistake 2 subtract 2 so this is one patch one patch, two patches not three and four I made a small mistake here and here we use just an alphabet of three letters and here 20 letters you get this very interesting self wrapping systems and here you use again three and 20 and here the knot is a bit more difficult to see but basically I try to highlight it by color coding that follows the index of the chain so it's basically this is one end and this is the other end of the chain and goes through so these are knotted and the knot has been evaluated by Luca Tubiana using the method that he developed to analyze the topological state and I think Christian mentioned that today on the method using to minimally frustrating distance of the convex hull of the knots so basically so now I want to show you an application of a knotted chain that is related to what I was mentioning in the beginning so with this technology we can design in principle chains to self fold into a given knotted structure and to control the position of the particle to the precision that we can predict exactly in space where the two ends of the chain will be so now imagine that you can construct this object in the lab and it will self fold into this structure as given here I call this temperature but you should just consider this as to the physiological condition where this chain folds naturally to the target configuration and reaches this state now imagine that you lock the two ends by cross linking by creating a cross link reaction that will topologically freeze the chain so now the knot cannot be undone unless you actually cut the chain itself what happens is that basically what we saw is if you now increase the temperature or in other words you bring your chain very far away from the physiological condition where normally it would fold the structure remains almost completely intact it stays there because this is a highly localized knot it's very well packed and even if you basically switch off the interactions between the particles it stays there because you created a topological entanglement that cannot be unbroken which means that this object can be used in completely different conditions than the one you constructed in the first place and just to mention that all I'm saying is not completely out of another planet we are actually working in Vienna with a group of Peter van Ostrom and Eric Reimelt to actually construct this chain of particles because another advantage of this system is that in fact you can both constructed on the micron scale just depending on how you represent this particle in the lab and if you do it on the micron scale you actually can see it under the microscope which is a huge advantage to follow in the experiments what happens to the system so as a biomimetic system this would be very interesting to see how it folds because it will also give a lot of information on how folding takes place on a simple polymer when you can look it up directly on an optical microscope so I'm going to finish now acknowledging all the people that I collaborated with in particular the people I work with in Vienna and all the other people will collaborate in particular Peter van Ostrom, Silvia Zia, Eric Reimelt who are doing the experiment I showed you before and I'd like to thank you for your attention