I would suggest you to really change methods in the same system I would start with an supervised machine learning and then if you have a ground truth also try to use some supervised machine learning techniques then it really depends on your data I mean and really depends on how big is your data and how complex are them in general for quite big data sets I would go for neural networks for instance but in other data sets it may not be the case it's really the case dependent okay and then there is another question which is what from Srabahani what kind of clustering would be useful to predict if we are on an unstable manifold of the phase space? An unstable manifold of the phase space okay I would a density based clustering would give you an estimation of the free energy in which with this free energy you can check if there is I mean as far as you have sampling also the most stable states you can check it if not there is no I mean you need that your data have some kind of trace that there is another state more stable otherwise you cannot learn it from your data okay good so I don't see any more questions on the chat so I think we can continue we can thank Alex again and then we can continue with the next talk so if Alex you aren't share your screen great and then Ali should be able to share his screen okay all right can you see my screen yeah we can see it we cannot see your face uh hold on well okay it's not working now okay so I mean we can hear you clearly yeah okay okay yeah okay good so the next talk will be given by Ali Hassan Ali who is also from the ICTP so please Ali okay let me all right thank you very much Giovanni and I apologize for my video not working so let me thank the other co-organizers in this activity especially Angelo for for putting this together and I also want to apologize for perhaps some technical hurdles that we've had today we're all in a learning curve with respect to virtual activities so what I want to tell you about today is regarding a problem that I've been interested in for for many years and that is the role of water and the goal of my talk today is to try and convince you that water the solvent around biomolecules in particular plays a very important role in in many things and so just to get you warmed up and to wet your appetite no pun intended um by the way if you have any questions at any point in the talk please feel free to interrupt I'm happy to not finish my slides today um so you know aqueous solutions are present in in all our daily lives uh I live in Italy and so in Italy I'm inspired by things like pasta and cappuccino and you know there's some very basic fundamental processes in physical chemistry involving boiling your pasta or making a good cup of coffee that involve things like you know the thermodynamics of surfactants how they interact with soap bubbles and how water interfaces with these processes so just to build your intuition a bit and to calibrate you on a bit of some numbers we can ask ourselves the following question which is how many water molecules for example are there in a cell and if you take the E. coli which is shown here in this bacteria which is shown here in this picture you can sort of count the number of different types of molecules that you would find there so roughly you'd have on the order of 10 to the 6 proteins you'd have roughly on the order of 10 to the 7 ions and all of that is surrounded by a big big big bucket of water and so the uh the number of water molecules in an object like an E. coli is on the order of 10 to the 10 and so the one thing I would like you to take away from this talk is that in all these models and simulations that we show and we discuss and when you think of processes in biology you always have to remember that of course these objects are very well hydrated and the water plays an intimate role in coupling to tuning the thermodynamics and the dynamics of the biomolecule so let's get into something a bit more specific and ask ourselves well what's inside a brain okay so these are images of on the left side of a brain of a normal person on the left and on the right here is the brain of someone who suffers from something called Alzheimer's so this is a neurodegenerative disease which leads to brain atrophy and neurodegenerative diseases have been you know mapped at the molecular scale to the formation of things known as amyloid fibrils this is depicted here in this spaghetti like a chain of mesh of proteins and if you dig even deeper and look even closer what you will find is that these proteins or these amyloid fibrils are made up of things known as beta sheets so these are it's a secondary structure of a protein which is held together by hydrogen bonds now all this stuff all these beta sheets all these amyloid proteins are surrounded by water molecules and so one of the questions that I've been interested in trying to understand is how water plays a role in stabilizing objects like this amyloid beta sheet so it's actually really nice to maybe go back a bit in history and to see what people have been talking about this and thinking about and if you go back you know three decades ago to one of the first papers by Michael Levitt who you heard today got the Nobel Prize in Chemistry many several years ago they performed their group performed the first simulations of a protein in water and compared it to simulations that had been done in the gas phase and you know it's very interesting to see here how you know the time scales of how MD simulations have been have evolved from three decades ago to now and so you know on those three decades ago doing tens of picoseconds was a was an enormous achievement and it was and one of the the messages that came out from this paper which is published in Scientific American was that you know water plays a very important role even though it makes it much more complicated to simulate a protein in in tuning the structure of the protein and you know there's been a lot of work over the last three decades from both the the simulation side theory and also experiments in in trying to understand how water plays a role but there's still a lot of interesting open questions in the field so this sort of leads to a motivating a bit of what I'm interested in and so I'm interested in creating aqueous solutions on the computer so I like to take different types of molecules so things like the amyloid protein that I showed you earlier on ions like the proton I'll tell you a bit about this and hydrophobic molecules like methane and inserting them into water and trying to understand how these molecules respond to the fuel of the water and vice versa so how does water respond to the presence of these molecules and secondly does water just play the role as being a spectator in all these processes so this probably doesn't need much introduction to you you already saw a good introduction from Alessandro Lio this morning so I'm interested in in in trying to design computational experiments where we try to understand how the complexity of water affects a different process and so we use a different types of flavors of molecular dynamics some classical when we don't have to deal with quantum mechanics for example things like bond breaking, bond formation and the real goal and this is what I want to try and show you today is to try to infer or come up with smarter water-based collective variables reaction coordinates okay and so in order to motivate this a bit I want to show you take you back several years ago it's a movie that never gets old for me and this is a very interesting problem in chemistry which forms you know the basis of pH so there's this dynamic equilibrium between neutral water and its ionized products the proton and hydroxide ion and this dynamic equilibrium determines the pH of water and so these were ab initio MD simulations that we ran many years ago and I'm just playing the movie now where you're going to see some interesting things happen in the movie you have the excess proton here on the left which is the hydronium mine so it's positively charged on the right side here you have the hydroxide OH- which is negatively charged and this is surrounded by a bucket of water and there are some fluctuations going on here where you see you know the the proton here is is is exchanging with its partner in a strong hydrogen bond and something interesting is going to happen here at the end of the movie where there's some fluctuation in the liquid which leads to these three protons jumping over at the same time and neutralizing the two ions and well the way we we studied this problem many years ago is the typical thing that chemists do which is you you take out the VMD you load the movie and you try to look with your eyes and try to identify where the fluctuations are happening what are their the relevant coordinates and I'm still a big fan of that but what I want to try and convince you today is that there are a whole range of length scales and time scales of fluctuations in in liquids like water which are very difficult to see just by using your eyes and so the combination of using chemistry-based approaches with the type of approaches that Alex introduced in his previous talk I think have a lot of prospects of understanding new physics and new and new chemistry so the the the reaction that I just showed you is not necessarily biological per se but there are many processes in biology where proton exchange plays a very important role and this is an example of one where it's well known that the amide proton of the amide bonds of proteins when it's exposed to solvent can exchange its proton with solution and this is thought to be catalyzed by the presence of hydroxide ions and this becomes a it's a very important experimental technique in order to identify which parts of the peptide backbone are exposed to solvent and which ones aren't so again that for this type of a process where you have some large fluctuations involving your protein and your water they become very challenging to just study by just you know using your eyes and typical chemical intuition-based approaches and so what I want to try and do today is tell you two stories if I get to it the first one is related to how water acts as a lubricant for biopolymers and some very recent efforts at using some more data science approaches to studying water networks and if I get time in the second part of my talk I want to tell you a bit about this problem that I introduced you at the beginning which is the optical properties of amyloid proteins and some very interesting questions which you will hear about in one of the talks tomorrow on the importance of electronic excited states in biology. Okay so let me get started and get to the problem so you know you've seen a lot of simulations today of different types of proteins and the typical thing to do when you have a protein let's say you have a protein in its folded state and a protein in its unfolded state is to try to come up with you know some order parameter that allows you to distinguish between the folded and the unfolded state and one of the assumptions of course that one makes when you do this is essentially you're looking in some reduced dimensionality of protein coordinates which I didn't notice p and you're essentially integrating out the solvent degrees of freedom and so I am interested in trying to understand how does that solvent modulate the free energy landscape of these polymers or proteins and so there are lots of different ways in which one can try to interrogate or understand how solvent you know affects the protein as you know as mentioned in some of the talks one of the first things you need to do is to try to come up with a relevant reaction coordinate or an order parameter or a collective variable that allows you to identify in your solvent degrees in your solvent space some changes that are going on and so I don't have time to get into the details but one of the things that we've found to be extremely useful is and that appears to give us much more information into the underlying free energy landscape of the solvent is by looking at topological properties of the water network around the protein and so the idea is extremely simple it's been used previously in other contexts that you know water is made up of a directed interactions because of the hydrogen bonds and you can map this to nodes on a graph where you have outgoing and incoming edges where the directionality of the edge corresponds to the direction of the hydrogen bond and if you imagine a protein and here this is a segment of this amyloid protein you can think about lots of different water wires or paths that connect different donors to different acceptors so every donor for example here the donor is an mh group and the acceptor is a co group can act as a source and a sink of hydrogen bonds and therefore different types of water wires so we've been studying the role of these of these water wires in changing the free energy landscape of proteins and I just want to give you an example of how it can change the landscape so this is some simulations of a some md simulations of a six amino acid segment of an amyloid protein and the free energy landscape is shown as a function of the distance between the two termini on the x-axis and on the y-axis is the radius of gyration and what these different minima here on this free energy landscape correspond to are different states or confirmations of the protein involving different amounts of hydrophobic contacts for example in this case in this case here in state a and in state c you have more hydrophobic contacts whereas in state d and state b the hydrophobic groups tend to be more exposed to solvent now the question is well where did the solvent go how does the solvent affect the free energy landscape well so in order to answer that question you need to know or you need to figure out which degrees of freedom you should look along the solvent coordinate and so again just to give you an example of how the solvent can affect the free energy landscape what i'm showing you here again is is is another reconstructed free energy landscape of the end to end distance between the two ends of the this amyloid protein on the x-axis and on the y-axis this is a a reaction coordinate that basically counts the number of paths that you can have between every donor and every other acceptor in in the protein normalized by a certain factor and what you see here i want you to focus on this oval region is that there are several minima along this solvent coordinate that correspond to fluctuations in the solvent coordinate but where the salt bridge is basically constant and so in in all these other if i go to the previous slide all these in the solvent coordinate is is basically collapsed in this figure over here and but when you when you projected out you see clearly that there are some other small minima that appear along the solvent degree of freedom so now in this system you have four amino acids actually six amino acids and there are already over 50 different water wires that can form between every donor and every acceptor i say this because just to give you a sense of that of where the the problem of dealing with a lot of data comes into the picture and so in order to to dig deeper into this and to understand a bit better about how the solvent affects the fringe and landscape proteins we had to break it down and go down to an even simpler system and so this is a system that has been studied a lot in the in the literature which is trialanine and trialanine can be classified into structures that are let's say more alpha helical versus ones that are more beta sheet and in this system they are a total of about of 16 water wires so there are 16 different paths that you can form between every donor of a hydrogen bond and every acceptor of a hydrogen bond and so the question that we were interested in asking was well you know can i look at the the water network around the protein this case is a small peptide and see is there a difference in the secondary structure alpha helix versus beta sheet and and so for this system i guess it's not too much of a surprise if you look at the the distribution of the the water wires that connect or that thread the alpha helix confirmation versus the beta sheet you see that in fact there's there's a gap between short paths and long paths for the alpha helix this has to do with its specific constraints of the alpha helix whereas in the beta sheet because it's more open you get the shoulder here in the beta sheet configure second structure that's not there in the alpha helix okay so so this is just looking at the the water wire distribution around the secondary structure but you know we can do a bit better and so i started talking to alessandro lyo who has developed them together with alex rodriguez who you heard from in the previous lecture who developed some very interesting methods on trying to handle and cluster high-dimensionality data and so one of the the techniques that they've developed is this intrinsic dimensionality estimator based on the two nearest neighbors of every data point and so i don't have time to get into this but basically by using the two nearest neighbors of every data point you can show that the cumulative distribution of this ratio can allow you to extract something known as the intrinsic dimensionality what this physically corresponds to in the case of our water wires or water network is it tells us how many independent directions do the water wires fluctuate in and so we we applied this to this alpha trialanine system so we have 16 wires we extract the intrinsic dimensionality of the alpha helix versus the beta sheet and you already see that there's a there's a difference between the two so this is already interesting because the intrinsic dimensionality is telling you about in the in the water space what the difference between beta sheet and alpha helix is and this sort of makes sense right because beta sheets are more open whereas alpha helix is more coiled and so you might expect something like that and then you can also construct free energy landscapes dendograms like the ones alex showed you and what you see is that if you look at the alpha helix versus the beta sheet this is along the solvent coordinate only you see that the alpha helix free energy landscape along the solvent is much more rough it has a lot of ripples that are very faint but it's markedly different from the free energy landscape of the water around the beta sheet which is essentially flat so there's only one minima and so what this is telling you is telling us is that basically the solvent at least at room temperature in a very faint way introduces some roughness into the free energy landscape of alpha helices one more thing we did was to compare how our beloved water wires compare with standard ways of looking at solvent around biomolecules so things like coordination numbers or essentially densities or geovars and what you see here is that the coordination number is rather dull and boring it doesn't really tell you about the underlying complexity of the free energy landscape and this again sort of makes sense because the thing that's contributing to creating this roughness of the free energy landscape is the orientational correlations of water dipoles around the protein and this is something that's averaged out in the coordination number but it's something that you get when you use the water wires and so you can now go in and this is why I think this combination of chemistry based approaches and data science is extremely interesting you can go in now and try to understand what these different clusters correspond to and what you learn is much more nuanced so what you learn is that the origins of the roughness of the free energy landscape is not made by very strict rules of this is purely hydrophobic this is purely polar context this is purely water what you see here is that there are very very subtle differences in the water wire distributions the number of backbone contacts and the number of side-chain contacts which in this case correspond to the number of essentially the hydrophobic interactions and so all these various things contribute to the coupled free energy landscape of the protein and its surrounding solvent okay um so uh Giovanni how am I doing on time uh yes you have uh I think five minutes okay fantastic so in the five minutes I will just tell you um uh something very brief uh but something that I find very interesting and and that is uh so I just mentioned to you a couple of indicators of what may cause the origin of roughness along the solvent coordinate there are also other factors that contribute to the roughness and something else that does is is understanding how empty regions or empty space looks like in in liquids and so if you think of a thought experiment where you put a hydrophobic molecule or an ion in water what you do is if you're interested in the thermodynamics of that well you will sit yourself in a box of water and what you will do is you'll wait for some time before you can form a cavity and this cavity is an excluded region of volume it's a hard sphere essentially where there are no water molecules inside here and by studying the statistics of the formation of these empty spaces you can learn something about the salvation thermodynamics of inserting hydrophobic molecules in water and so this is something that has been studied to death by many people in the field but typically people have usually mostly only focused on you know nice spherical objects and we all know that biomolecules are not spherical cows and so for a while now I've been working on and thinking about how realistic regions of empty space look like in liquids and I won't get into the details but so this is just a a sample obtained from a molecular dynamic simulation of how realistic regions of empty space look like in water and so these these are distributions here you don't need to worry about the the mat just focus on the water ones where these distributions tell you the probability of finding a normalized volume of void it's normalized by the volume of a water molecule and what you see here is that there's a there's a peak at small values sorry sorry I should point to the water and there's a tail to larger values which correspond to these types of voids that look like this so these are very branched dendritic shaped voids and if you stare very carefully you might be inspired to look for interesting resemblances of this to a basketball player and this guy here on the left is a small dinosaur and if you're even you look even harder what's curious about this is that these dendritic shaped voids look like small polymers small molecules chemical molecules and so this is something that was done in in collaboration with former postdoc Nergis Ansari who's in the audience and one of the things we asked was well can we find a shape of empty space in the liquid so without a polymer that resembles the shape of that you find around a polymer and in fact you can and you can translate this into something more thermodynamics which is the following which is what is the salvation energy of solvating a hydrophobic polymer like this one here and by the same time you can also ask what is the the free energy required to create an empty space like this in water and what's interesting is that you find that you know these two numbers are are essentially consistent with each other and so they are these what rare fluctuations in water itself that that create shapes that are consistent with the thermodynamics of solvating small hydrophobic solvates okay so I actually don't have time to go through all this so I'm going to skip it and would rather take questions oops so afraid my computer is frozen okay okay let's go to the end and so I basically I didn't get time to tell you about the first one but what I tried to tell you about today is how essentially water plays an extremely important role in in coupling to the fluctuations in in biological matter it affects the thermodynamics and the dynamics and there's still a lot of interesting open questions in the field and I think there's a lot of interesting synergies between combining chemical intuition based approaches as well as data science approaches to learn new chemistry new physics so with that thank you for your attention thanks Ali thanks a lot for being in time so now we have time for questions so just write on the chat if you want to ask a question you can either write the question and I will read it or you can ask me to speak okay so there's a question so from Davide so what could be the outcome of the fact that little polymers can occupy the void left by water okay what could be the outcome well so there are two things one is it's a there's a question of just thermodynamics right so yeah so let me let me answer the first part so you know the way typically in in the physical chemistry community the way people typically have thought of salvation of hydrophobic molecules is that you need to there needs to be a huge reorganization of the solvent of water in order to facilitate the presence of the hydrophobic molecule and what we're what we're saying is that it's it's actually not so much like that for small molecules it's that you know the intrinsic fluctuations in the liquid can create shapes that can facilitate the presence of those molecules without having without paying a significant energetic cost okay so that's that's the first that's a implication yeah there's another question from Davide which is maybe ready to ready could it have an outcome in the drug discovery field could it have an outcome in the drug this is a well a difficult question maybe I think that so the question is in in the drug discovery field what would be interesting to think about and wonder is when you have a drug interacting with a protein how are the dendritic voids and empty spaces around those two objects talking to each other okay I think this is is not understood you know there's been quite a bit of work trying to understand how dielectric properties for example between two proteins or a protein and a drug drug change when they come into close proximity but where I think this has a possible relevance is you know really trying to understand how these these fluctuations around the drug around the protein may couple to each other okay then there's a question from Lorentz so that is with the aim of reducing the computational cost so what do you think about the hybrid salvation I mean for example a shell of a lot of water around the soil to all surrounded by coarse-grained water molecules um so I think it it really depends on what your questions are and what you're interested in and so I'm generally not a fan of coarse-grained models I understand the need to do them you know what I would say is the following I think the let's say the building evidence from experiments in theory is that water around biomolecules can can feel orientational correlations up to about 15 angstroms okay so if you think that these types of long-range orientational correlations will affect the let's say the process that one is interested in then I would say one has to be very careful about how you choose the thickness of the hydration shell okay but you know as I said I don't think there you know I can equally buy the argument of you know if you want to simulate large complex systems it obviously makes sense to do some type of coarse-grained so I think it's it's really depends on your question okay then there's a question from Andrea in atomistic simulations how different water models for instance tip 3p or spc affect these properties and or analysis yeah that's a that's a fantastic question and so basically the bad news is that tip 3p which is the model water model that's used in in many biosimulations is quite horrible for for water alone okay and now it depends again it's sort of similar to my previous answer it depends a lot on whether one is interested in thermodynamics or dynamics for thermodynamics you know I think you know choosing the the the water force field with the appropriate protein force field you sort of more or less are able to converge similar results when you look at the properties of the protein now on the other hand if you look at the if you're interested in understanding the properties of the solvent around the protein then it can be very sensitive okay and it can vary from one water model to another so so yes results can be sensitive to the choice of of your water model particularly the dynamics for the things that we looked at which are these topological properties they are much less sensitive because it's you know most water models have more or less gotten you know the the mostly tetrahedral networks okay with with some defects and so and so far so that's more or less correct okay then Sudarshan would like to know what tool did you use to get the hydrogen networks around alpha helix and beta sheet ah so I I once had a very good PhD student who who who left for North Korea and he wrote all sorts of things for me in C++ but there there are lots of tools available hours a much better much more efficient ones by other people who are developers so yeah okay then there is another question but it's it's a duplicate basically what is the basis for the selection of water potential models yeah I think this is uh it's a repeat so yeah yeah yeah good so any other questions from the audience or comments okay there is another question from Marcelo so is there a linkage between the void of water molecules and the polarization of them if so how would it be how would it possibly be connected with the molecules you've shown yeah that's a that is a great question and so in fact they are we have someone unpublished or ongoing work right now that examines the the extent of charge transfer between water molecules closed to avoid versus being far away so you know you can think of a void as as a as a sort of an enclosed a short length scale region of analogous to an interface okay and essentially there is a polarization at these interfaces and around these voids and where I think it will play a much bigger role is when you start to introduce charged molecules so if you have a molecule with a you know well it doesn't actually have to be charged yeah something with a dipole moment a quadruple moment may couple in a non-trivial way to the the void and its corresponding charge polarization but that's a good question yes okay good then there's another question from jamal that is what kind of interaction will it have in empty spaces uh sorry which kind of interaction will it have in empty space i don't know jamal can you yeah could you clarify what you mean okay here jamal so okay good so maybe we can thank Ali again and then proceed with the next talk so the next talk will be given by angelo so i think you can share your screen can you see it yeah clearly so the last talk of today will be given by angelo rosa who is also from the physics and chemistry biological systems at so yeah thank you Giovanni thank you all for listening especially for asking very nice questions i'm very happy about that they said it's sort of an experiment for me this event so it was actually it was very nice what ali said at the very end because he said i don't like very much course grade models and actually instead i do and so that's a nice way of sort of connecting to the previous talk and also to connect it to the talk which christian micaletti has has done in fact the the first part of my talk it was very short but it will illustrate a little bit sort of a few things about polymer physics in general and why actually you can use course grade model to learn a lot about the physics of polymers okay and why they make sense i mean this is probably a trigger for many of you but since this at the origin was meant to be a school so i preferred to keep also some pedagogical opportunity to say something so briefly i mean i'm sure here everyone knows what a polymer is so basically it's a it's a big macro it's a macromolecule it's a big molecule and is made of out of a polymerization process so you just can put one after the other some minimally units which conventionally we can call just monomers and so they exist in different i think they exist in different architecture and also what is very important in different states so if polymers are quite diluted in dilute in your solution so you have a sort basically you have a gas the properties are very similar to the ones of a gas then if you start increasing concentration you go to a liquid like state and then if you increase the concentration even more you got something which is pretty much like a solid states for instance rubber basically is made of a polymer so join together and but it looks like a solid at least on some time scales and length scales of course now we we have biopolymers and we have seen a lot this morning also this afternoon so biopolymers are proteins nucleic acids and actually nucleic acids it will be part of my talk and the second part and we have chromatin so chromatin actually more chromatin than DNA will be the second main actor of my the actor of my second part of this talk and the chromatin is basically is a is a is a is DNA plus some proteins so but I mean to to to to all extend is is a polymer itself so now why I mean what is polymer physics so polymer physics is basically is the study of is a polymer conformation so if you take for instance a very simple polymer which is polyethylene the single monomers I mean the two single monomers when joined together they can exist into two different actually in three different states two Gauss according to the orientation of the bond in one trance which has a smaller energy and depending on how these bonds are arranged I mean they I mean a long polymer chains can attain a a high number of conformation so it's an ensemble of conformation we don't have only one unique conformation and so the start the polymer physics I mean the object of polymer physics is the study this is the sort of the statistical mechanics of starting from this conformation as you can imagine based on the n is the degree of polymerization of the polymer chain so these polymer conformations that grows rapidly are basically the increase exponentially fast and so then you can use the tools of statistical physics to study any polymer problem I mean where physics enter as an actor so there are the basics idea were firstly formulated in the I mean between the 30s and the 60s of of the previous of the 20th century by many authentic over like Kuhn, Eugnes, Schochmeyer, James, etc while let's say let's say more statistical stuff like the study of polymer solution polymer melts and the role of entanglement we have listened to you stalked by Christian where we talked a lot about entanglement were formulated by many people like Edwards, Declasdo and especially the Gen who got actually the Nobel Prize for his work on on such kind of stuff so let's say you know if you want to formulate a polymer model for sorry a physical model for for polymers you start from something very simple and there are basically two let's say two simple polymer models one is the freely joined in chain where basically the joint between two two two monomers is completely free to to to rotate into the space and another model is the freely rotating chain so now this angle theta between one bone and the next one is a fixing space is not allowed to to take any any value between zero and pi while you have still some freedom orientation in the azimuthal angle phi of phi and which can still move between zero and two pi and now what you can ask is what is the typical size of this polymer and you can do calculation etc in this case and you can see that in the first case basically it's just a it's from the the free joint in chain is just like a random working space so just it increases linearly with number of monomers by some pre-factors which is the average bond length between two monomers well in this other case the chain is slightly I mean in general depends on the on the value of this angle theta it's more or less stiff but still it increases like n in terms of the number of monomers so now all these two models actually uh let's say they belong to the same universality class in sense that you can define a typical length scale for each of the two model which is called the Kuhn length which is a measure of how uh let's say of of the rigidity of the polymer of the local rigidity of the polymer and then everything I mean the typical size of the polymer can be recast in this universal form so and where nk is total number of Kuhn lengths of Kuhn segments if you want of of your polymer so in this tells us very important things that somehow these laws are sort of universal I mean you can still have basically the same model described the polymer chains regardless of the microscopic details and and this is oops ah yes and and this tells us a lot I mean about what polymers are basically polymers are fractal objects and if they are fractal objects of course this is very nice because now we can employ to study them all the ideas that comes out of fractality on the and the self similarity and basically when employ things like those in order to study models now for real chains now by real chains I mean the following in the previous in the previous slides here I have basically I mean any two monomers can just occupy the same portion of space right there are no correlations so two monomers can overlap together this is of course not very realistic and while we need to exclude those conformation which where any two monomers can share the same portion of of space and in this case so it comes I mean something which becomes very more difficult because now all these kind of models cannot be solved exactly and so in order to get an idea of what's going on we have to employ either mean field theories like the ones that were formulated by Paul Florin another Nobel Prize winner actually for his work on on on the physics of polymer on statistical mechanics of polymers and so you do so if you apply this tool you know I mean you can get that the typical polymer size now is no longer increasing like the square root of the number of monomers but it's different power law means meaning that the polymer is more swollen or you can employ as I said since polymers are fractal objects you can employ something very sophisticated like like basically renormalization group and sorry I just want to okay like renormalization group and if you employ renormalization group it means that you can basically use all the tools that were derived in the in the 60s by guys like again the gen basically and the croissant and in order to what you do basically in you can have your polymer chain then you construct sort of super monomers in such a way that you make a coarse graining of of your polymer chains so what you do you coarse grain your monomer and you also coarse grained interaction and if you do that you can apply iteratively this this procedure in such a way that you arrive to an estimation of how the chain grows inside with the number of monomers and the result actually becomes pretty accurate because you get an exponent which basically confirms the mean field but it corrects it because now this is rigorous and at the same time it tells you that an important thing that basically you don't need too much information on the let's say on the local interaction but what you need is some sort of simple model because then only interaction are renormalized so then you get the right answer so that's why somehow you can translate all these ideas also in computation you can use especially for the large-scale behavior you can use a coarse grain model and you get study big system and one typical so and then I show I go rapidly to an application of this idea where I can employ actually where I need actually to employ a coarse grain system because the scales are too big and the system would be too large that a fine grain or a full atomistic simulation is impossible or full atomistic approach is impossible to do so the the system yeah sorry okay sorry the system that I have in mind is that the problem of chromosome folding so what is the problem of chromosome folding so so far Cristian also has mentioned here in this morning so you have DNA but in cells I mean DNA is quite complicated since that you have not only bare DNA but you have DNA plus some proteins these proteins are called estons and the estons sorry the DNA is wrapped around the estons and they form a neck a sort of necklace this necklace is called the 10 nanometer fiber because basically the let's say the average diameter of this fiber this fiber DNA plus protein is about 10 nanometer then what it is observed that in some specific condition this 10 nanometer fiber is folded into a super fiber let's say which is called the 13 nanometer fiber because again the diameter of this fiber is around 30 nanometer and then I mean under some condition these things take the form of chromosomes some of these let's say these x shape chromosomes x shape that you can find in test books okay so so that's a basically the biology of chromosomes now what is interesting about that is the following it was observed now more than actually the ending of 19th century by these two guys Karla Raab two german biologists Karla Raabol and Theodor Boveri that actually chromosomes are not sort of randomly organized inside the nuclei of the cell but they take a very specific shape so that at the time was a really generic instance that they were studying that from you by using optical microscopy so the study nonetheless I mean they could predict something they could observe some things but I mean it was not very quantitative in order to get some I mean a more quantitative picture we need to go to the 70s I think where these two german guys actually two german brothers they invented a technique which was very clever in my opinion so what they did they used some laser beam on the nuclei of some cells I don't remember which cells were where eukaryotes so cells with the nucleus and they beamed the nucleus of the the nuclei of this cell so they said that the following so if the hypothesis of let's say of Raabol and Boveri were correct so namely if chromosomes are not just randomly organized but they have a structure inside the nucleus so then we should observe the following so if you imagine that the chromosome are just mini chromosomes just like a tangle of structure of the DNA of fibers and if you beam them so then sometimes you destroy I mean the laser is so strong that destroys DNA so it makes a breaks so I mean if you do it just in some random spot then sometimes you eat the chromosome sometimes you eat another chromosome because they are all mixed like a spaghetti dish okay instead if they are organized then you should I mean and if you beam then again then you should only destroy a few of those just a very small number and actually that was the outcome of the experiment okay that was done back in the 70s so this picture of non-random organizational chromosome was confirmed actually by another technique more more sophisticated actually which is called fluorescence which is called fluorescence in situ hybridization where basically you can design specific probes for selected sequences for selected DNA sequences on chromosomes you can sorry you can design probes with different colors according to the sequence you want to probe and then in the end by using high fluorescence microscopy you can basically see chromosomes inside the nuclei of the cells and so this is the picture you have here on the right on the bottom corner is a sort of re-elaboration of one picture that they observe by high fluorescence microscopy through fish and here each color corresponds to different chromosomes meaning that the chromosomes actually they are not like spread inside the nucleus but they are organized in some specific portion of the nucleus that this guy's called chromosome territory and actually the the the presence of territory is quite important because it correlates with so it's not random inside the cells in sense that they found some correlation between big chromosome and small chromosomes sometimes big chromosomes so in I mean most of the cases big chromosomes are found towards the periphery of the nucleus as small chromosomes toward the interior and they are functional so in sense that if you destroy this kind of organization or if you damage this kind of organization this is associated to potential diseases and also to to the death of the cell so then this is for instance another observation they made that actually mammals which are let's say which are very similar or very coming closer and from the evolutionary point of view and but they have developed for I mean for reasons different habits like for instance one mammal is diurnal one mammal is nocturnal the chromosome organization in in those cells for instance retina cells and is different and the response to this to to to how these mammals have evolved in the course of their life and and these are this is another technique that was developed this is actually much much more recent than fish and this is called the chromosome conformation capture technique so these techniques allow you to detect how much somehow frequent the DNA interacts in the nuclei of the cells and this is done in this way so you use formaldehyde in order to make cross links of DNA inside the cells some enzymes which are called restriction enzymes that cut all this fragment and then you do a bit of the say of post processing of this fragment you know basically you amplify this fragment and you detect the frequency of how I mean how much frequently these these fragments appear okay and the idea is that fragments which more frequently interact they should appear more frequently in your in your statistics now of course I mean you have a lot of these contacts between fragments which are very close in sequence I mean basically in the fragments of DNA which are very close in the sequence of chromosome interact frequently and this is this appears in this contact matrix so where the diagonals is very populated but there are also non trivial contacts instead of that contacts which are so there exist contact which are between DNA fragments which are very far in sequence but they are close in space okay and this concept tells us that there exist a non-random organization for chromosomes so and this tells us I mean if you want these compliments what high sea oh sorry what fish has told us that there is no normal organization of chromosomes so now can we understand that that that was basically the purpose of my investigation of what I will present now can we understand I mean by some just simple physical mechanics the presence of a non-random organization of chromosomes inside the nuclei of the cell so now the problem is interesting from by many point of views and indeed it's because of the following so each so if we take just an ordinary human cell so the ordinary human cell contains about six billions base pair of DNA so it's about one two meters of DNA inside each cell and so the cell is contained inside the nucleus which is only 10 microns of diameter so you have let's say you have like I mean if you want to make the proportion it's like putting stuffing I mean a 100 kilometer slope inside an ordinary backpack so and as also Christian has pointed out before so there is a lot of problems with that because you create a lot of entanglement so that's why the problem is so interesting from the physical point of view so if you want is another proportion it's the same distance as between the center of the sun and the Uranus and the nucleus is just the so I mean there is a really huge gap in land scales so in order to better understand the problem from I mean to cast the problem into a physical problem we just go back to what happens during the cell cycle so the basically the chromosomes are very dynamic so we have two phases during the life of the cell one phase is called the mitosis and it's where chromosomes take this peculiar shape like this X shape and then you have interface and it's during interface that chromosomes behave as I said territorial so they form this territorial organization what it happens in between during mitosis and the chromosomes when they enter interface is that they start to open from this X shape they have during mitosis and do some dynamics inside the nucleus and then form territories so you know if you want to to to to to get a clue I mean what's what's going on then you can do that actually it's what we did at that time with with Ralph Everest who is also going to to give a talk in this conference this event was the following so basically we simulated the let's say the transition from the mitosis to interface in order to see if we saw I mean by using a polymer physics model in order to see if we could get something about the formation of the territories an idea why I mean why territories form in order to do that we use now I mean as I said a very coarse grain model because I mean as I said that each chromosomes this is for for the typical mammalian cell and each chromosome here it's about 100 million base patches it's an enormous system no way to do that let's say by using the standard simulation so before like using water expertise so many things like that so we need to do something very coarse grain and the level of coarse grain we used was at the level of the 30 nanometer fiber namely if we do if you do some mapping means that we used a chain of beads for model one single chromosome and each bead map to 3000 base pairs so if you do then the proportion that means that each chromosome here each chain is about 30 000 monomers at the time we use the four of these objects which are totally they are all the same they they it's a normal polymer so there is no chain there is no information from the sequence it's it's very basic so in the end the old simulation contained about 120 000 monomer particles and the chains were arranged let's say randomly inside the box with simulation with periodic boundary conditions and otherwise we arranged the chains as I mean accordingly by using a very simplified model for the mitotic organization and let the simulation go what we used then was a standard Brownian dynamic simulation of a generic as I said a generic polymer model it's called the the Kramer-Grest polymer model basically as I said is a Brownian dynamic simulation so you have a Langemann equation with some potential between the monomers with noise with zero average and standard and delta correlated in time and in the monomers so that the force will let's say it's very simple and it's something very standard using polymer physics so you have a chain connectivity of course this is very important where you use what is called the Finet potential which is I mean if you are unfamiliar with that it looks a bit strange but basically this potential was done in such a way that two monomers I mean two bonded monomers cannot go too far we don't use harmonic potential because because the presence of this logarithm term basically if I mean the distance becomes too far then this potential may vary so that's why we don't want that because that's a crucial part of the story then we have some standard bending stiffness for the chromatin we just tuned this parameter in such a way that we matched some experimental observation from from the literature we imposed the number of monomers and the sides of the box inside of the periodic box in such a way to mimic the original I mean what the average density of DNA or chromatin inside the cell and then we imposed hardcore repulsion between monomers so basically when these two monomers fluctuate and they do bump into each other they cannot cross and that's why it's so important actually to use Finet because if you use a potential which is a for bonding interaction which is just harmonic basically you can basically what happens you can break topology because the monomers in principle can go quite far apart in principle if the the potential is not too strong and then you can have a chain I mean two chains can pass through each other we don't want that okay so that was our minimal ingredient so if you do that basically you let the simulation run under these you're starting from this initial conformation and you end up with something which looks like that so basically each chain maintains I mean from the visual point of view maintains its identity and as you said it's very similar to what can you observe in inside the cell so you you see territories but can we be more quantitative than just than just pictures so yes one important thing here is how which is I think is a bit sometimes underestimated but it's a very important point what is the typical time scales you can do in the this simulation because this is of course constrained simulation so basically you need to fix in somehow I mean some way basically diffusion coefficient of your of your monomer in order to do that we did the the following so in the literature we found some data on where people were monitoring the mean square displacement of a single gene on some I think it was east chromosomes in time so they used the microscopy in order to to monitor how these things displace and they basically then measure the mean square displacement in time of of of these logs so then what we did we actually simulated these the same system using our model and we just fixed the time scale in order to match the experimental observation actually here there is a point what we did basically which was only a shift in the x scale without shifting on the y scale so that means that we had the complete control of the of the of the spatial scale there is no fit on spatial scale there is only fixing the the time scale and though and so by this problem so if you if you want I can give you more detail later so by this protocol we were able to show that with this setup you can draw you can basically reach I mean at the time it was like about three days in real time so that's was how we fixed the time scale of our simulation and that was quite important because then you see that you can reach macroscopic time scales and so these all these things make sense and then we can compare to experimental data so that's these are these two pictures are the following I'm going to explain a bit more in detail so here the lines are the results of our simulations the symbol are the results of experiments so in the top panel so experiments are the mean square spatial distances between two loci on on some chromosomes so sorry I I don't know if I can yeah so the different colors here sorry it's not indicated in this figure but the different colors means different species okay so red colors is east saccharomyces cerevisia and here blue or cyan is man homo sapiens the gray the green one is also mo sapiens and the brown is drosophila melanogaster and the lines are the results of simulations for the same quantity namely the mean square spatial distance between two loci on the same chromosome as a function of the genomics distance between them this is it says a standard quantity you can measure in polymers to to basically to read the statistics of your polymer chains and as you can see here that the results of simulations which are given by the the lines match match the results of of the experiments so we were able to provide a quantitative so basically the our model is able to summarize in a quantitative way the outcome of experiments from the further structure another of course I mean one set of experiments is not enough so we we saw by the same simulations what it happens to when you measured the how how to chrome sorry how two loci the same two loci the same pairs of loci interact in space by comparing to results of this other technique chromosome conformation capture that I mentioned at the very beginning and and also here the result is is in agreement with the experiments so I guess Giovanni is appearing so how much time do I have one minute one minute okay no I'm I'm done and yes and what is important here two three minutes is okay no no it's okay I can finish here it was just a part of showing the results of this simulation so and what's what's important here is also I mean this kind of behavior you observe here because it's it's not by chance so we have an explanation a quantitative explanation why observe I don't have the time to to go into details I mean you can contact me in case you are interested or we can discuss later in the in the questions time so the kind of expanse you observe here which is that special distance is increased like two over three and the contact frequencies the case one over l tells you that basically this is a no standard polymer systems it's not gaussian it's not self-aware in work it's something completely different we have a quantitative explanation and quantitative mod mod quantitative model basically for first principle why these things are like these well if you want I can tell you later on another day but this something's very interesting because then allows us to do some specific mapping and to construct a more coarse grained version of this system and to simulate bigger system otherwise we can do the opposite and and we can do also some fine graining by starting from same model by going to smaller scale because now that we have a sort of intermediate scale from 13 nanometer to something larger you can do also the opposite and don't then go below by using some very straight forward fine grain and that was we did it a few hours ago sorry I don't have time to go into details but the fine grain basically allows you to to to study smaller scale in a very systematic way and also to explain how certain genes yeah in a very in a very simple way basically this is all a mechanistic effects so at this point so I just want to yeah this is the explanation blah blah what I wasn't mentioning before but I just want to conclude by acknowledging yeah the two people that were really involved in this work first of all Ralph which is going to talk in a few days I think on Wednesday and Ana Maria was a postdoc here in CISA I left a few years ago and now he's working in molecular partners AG in Zurich and of course I want to acknowledge many computational resources I use in these years so thanks for your attention and thanks Giovanni for chairing the session thanks Angelo so now we have time for questions so as usual just write your question on the chat so just a question I don't know if we were able to see the arrow no yeah oh yes okay I can see it now this is you know just because I didn't I don't know I didn't know so questions or comments from the students it's very important curiosities maybe I will start with a question so how expensive are these simulations well I don't know I don't know I know but yeah it can be very expensive actually well okay the first simulation I did or now but it's now I'm quite told it's about I think I spent about a month or some class there for simulating these these you can still see the screen here right yeah so when I did the simulation when I was a postdoc in the resident so that was pretty expensive I think I spent about a month for doing the simulations and yeah if you want to relax okay first of all if you want to relax completely this system this is impossible okay so then you you can relax some up to some length scale and then okay and that was the point of why these things work actually because it actually is not relaxed that was the time to explain that into details but then you can do as I said you can construct a protocol which is in order to to let's say to to use a sort of multi-scale modeling and that's this much like expensive and you get the same results but then you get the complete let's say this confirmation from basically with a few days of computation so by then you are using Monte Carlo so you are building another model which maps into these and by this no it's not micro dynamics Monte Carlo so you don't have access to dynamic of course then from the same structure that you have built by Monte Carlo then you can use you can do the dynamics if you want but then yeah many analytics a lot yeah I see then so there is a question on the chat from Fahad asking if you could explain the L to the 2 3rd low yes so actually as I said so I was a bit well I was not really careful here but it's a bit so because I didn't have time so but the fact is the form so if you so the idea is the fact is fun so you start from these conformations right which are obviously are not in equilibrium and so then you let these things relax to some point whatever this point is and then you end up with this okay but then again as I said before this confirmation not the equilibrium sense that they are still keeping memory of the original conformation so basically here what you see here somehow is what you have put into the initial state so then you say okay but this is a bit disappointing right because I mean so what's that and the fact is the following so and that explains also these exponents so suppose you do the same this kind of sort of experiment let's say get on an experiment so what you have what you have here is you start from some conformation which is not in an equilibrium is this kind of roles if you want then you know that just by entropy as sooner or later you should end up into this kind of conformation where everything is completely mixed just because of entropy this is something that is perfectly known I mean where polymer have to go but before doing that I mean before reaching this state you have to go into something which resemble more like this where sort of you have some partial let's say relaxation of the structure of the original structure but you don't have the relax the topological relaxation of the topology namely these things these objects at the very beginning are not entangled let's say are not linked with each other and so they maintain this alinkness let's say for a long time right so if you it's the if that's the case then you can just say okay I don't okay then you can estimate how much it takes to relax this topology is very long time but then I can say okay then I don't I don't care about the fact that these chains have some ends so I can just forget about the ends and I can I imagine that my system is not a system of linear chain unlinked and entangled linear chains but are a system of ring polymers where rings I mean that I unlinked and unnoted because basically if you want it's it's it's really the same thing and so then I let these things to relax okay if you do that then I can say this system of unlinked and unnoted rings have something to do with the simulation I did before let's say for the for non-equilibrated linear chains and if you do these experiments you base the same simulation I mean same setup the same model you end up with something like this so basically equilibrated rings okay behave like let's say non-equilibrated unlinked linear chains so this is the same measurement I showed you before so the mean square internal distance is between two loci as a function of if you want of the genomic distance so now if you do that now we have a reference system which is an equilibrium because it's a but it's not linear chains it's ring polymers and then you can now there is a lot of literature on that so now a system like this has to be a completely different from the equivalent system or linear chains they should be more compact and they should display this precisely this exponent namely they must be compact if you want they are space feeling because this sort this exponent tells you that ring polymers are space feeling and they and the the contact frequencies between loci has to decay they has to decay like 1 over l and not like 1 over l to for instance 1.5 which is the typical behavior of a random walk what you would expect in between contacts on on an linear chain if the chain was a random walk except for the walk would be even worse would be even more steep than that so that if you use a model for rings which are naturally if you want a tutorial because they are naturally compact so then you get an explanation for this kind of experiments which is quantitative in this decent equilibrium system then you can do thermodynamics statistical mechanics so this and now there is a lot of literature on on the probably roughly mentioned with that I don't know so you know if I answer the question there's another question by the same person it is do your simulations agree with loop extrusion theory yes they the good question there is no loop extrusion imposed here and the I think my answer would be no in the sense that this is something that actually this pertains to some to a non-equilibrium mechanisms which means that I don't expect that to become compatible with that but of course you can impose that it's it's it's pretty straightforward because now we have if you want is a sort of ground model then you can impose loop extrusion then it's another another question is if the structure you get by loop extruding by using loop extrusion on some initial structure for some time does it look like this one that I'm constructing here maybe this I don't know but it's an interesting question actually I we are thinking about to normally in this direction but so that's another point but I agree that is yeah now loop extrusion is quite popular subject so I agree it's an important point okay good so I don't see any more questions in the chat so if there are no more questions I think we can thank Andrew and all the other speakers again and then I saw Adi appearing maybe do you want to say something no okay okay good so thanks to everyone and yeah the school will continue tomorrow with the advanced lecture so see you tomorrow morning thanks everyone for participating ciao bye