 Welcome back everybody, so in this talk I will tell you a few things about how to use polymer physics in order to understand the chromosome organization inside the nuclei of the cells. So this is now a very nice and very developing topic and there are many research group working on this. So before moving to the specific subject I just want to tell you a few things about polymers for those of you that you know too much about that. So of course I mean polymers are central in let's say in soft matter theories and are also objects of very extensive computational modeling so which is probably almost of a great interest for this workshop. So polymers are, what are polymers? Polymers are big molecules which are made of many repeating units. Each one of these repeating units is called generically monomers and because of these chain reaction which is called polymerization you get from one single unit I mean through this chain reaction a very big molecules and in principle I mean this chain reaction can go on forever so in the end you have molecules composed of many many single of these repeating units. So polymers I mean depending on the constituents they can be relatively simple like polyethylene like where you have I mean single repeating units which is ethylene which repeats many many times or it can be more complicated okay and here you have examples of more complicated polymers that exist in more complex architecture like for instance alternating copolymer where you have let's say repeating units like AB, AB, AB etc or they can I mean the ordering of these constituents units can be just random can be organized in block and they can also be let's say more complicated not just linear but they can be like branched or circular I mean not the example of this but I mean they can be existing many many architecture so it's very complicated I mean let's say the kind of architecture you can have in polymer domain. Then polymers can exist also in different states so you can have a gas of polymer for instance or you can have a liquid of polymer like a similar solution or melt and they can be solid okay for instance the main constituents of your of the tires of cars are made of polymer which are cross linked in such a way that you keep the structure together lacking a solid although they are not really solid since there is no a really longer range of order in that but they can be considered solid since that they they have elasticity or I mean things like that. So now to our concern specifically for this workshop there exist of course I mean biopolymers and biopolymers are of these three different kinds let's say they there exist proteins where I mean which you will have heard about I mean in other talks more about proteins there exist nucleic acids and nucleic acids are more I will tell you a few things about nucleic acids during this talk and there exists chromatin okay chromatin is basically the basic constituent of chromosomes and let's say it comes out of DNA plus constituent proteins and these constituent polymers are necessary in order to fold the DNA inside the cells but all of these I'm sorry all of these are all of these are I mean besides being biopolymers they are polymer nature so they share many of features that normal poly that I mean the normal polymers that I told you before so now one essential feature of polymer is that because you have a small fluctuation I mean between the orientation of the monomers that constitute the chain it happens that polymers do not exist typically in one simple conformation okay but you have many actually it was realized a long ago that the number of this conformation is high I mean it's potentially high in the number of monomers so that means that and it was the basic ideas formulating the I mean from the 30s to the 60s by I mean all this bunch of outstanding people that basically can treat polymer physics like statistical mechanical problem okay and that was what I mean the fundamental idea that was of course developed by many of these people but I mean basically earned the flurry and noble pricing chemistry where he applied the statistical mechanical ideas to study the polymer problem and there were other developments from the 60s to the 90s where more advanced concepts were applied like correlations entanglements that were developed especially in the works by Sam Edwards, Pierre Gilles Degène and Decloseaux and they were so important this I mean the contribution that earned I mean Pierre Gilles Degène a Nobel Prize in physics now for applying the statistical physics concept to the study of polymer conformation so it's a very it's a very important subject I mean in in in soft matter so now there are many models I mean that you that you can direction statistical mechanics in order to understand the polymer properties the fundamental model is the ideal polymer model by ideal I mean that what it implies that you I mean this is as fundamental as the ideal gas model in statistical mechanics in sense that you completely neglect interaction between the different monomers and you treat polymers as a string a chain of beads and sorry a chain of of links and these links can take any random orientation in space so I mean this is a relatively simple problem to treat and then if you use this formula to understand that basically the typical chain conformation for polymers to be the same over and over so this if you neglect if you neglect interaction between the monomers there are more complicated relatively more complicated models that you can introduce for instance the freely rotating chain but the important thing sorry the important thing of this model is that you are neglecting interaction so in the end you always end up with a linear relationship between the typical chain size the typical square chain size and the number of monomers okay so this is relatively so this is a strict a strict law that you can derive from this from this model well a typical feature of polymers that they are the obey scaling variance in sense that they are fractals which means that a single part of a polymer looks like the old part so and because polymers sorry oh sorry I heard some boy so because polymers are basically invariance well sorry before before saying that I have to tell you that if you start introducing exclusive volume in the in your model so things become slightly more complicated and of course this is a necessary ingredient if you want to understand the properties of real polymers because of course I mean two monomers cannot occupy the same portion of space and immediately you end up with a scaling namely with you end up with a relationship between the typical chain size versus the total number of constituents that it's no longer does not longer respect the random workflow but it's a bit larger than that so that the effect was highlighted by flori and course realized that basically the properties of polymer do not I mean the large scale properties do not depend really on the specific interaction of the between the constituents but it depends on a very few essential parameters okay and in this sense you can apply if you let's say renormalize this interaction you can apply the same tools of course grading renormalization group and basically you can use the same tools of just some typical tools that were derived in statistical physics to derive the properties of polymers that was done in many works in the 60s to the 70s by especially by Pierre Gilles DeGeneres and Saint-Maitreaux okay that derive the complicated that derive I mean a very full complete understanding of of this of the properties of real chain so this was a very I mean superfast introduction so of course it cannot be exhaustive but this is somehow necessary to understand a bit on the properties of chromosome folding and where you can apply you can use polymer physics in order to understand how chromosome falls inside the nuclei of the set sorry so what is basically the problem of chromosome folding okay so first of all what are chromosomes as I said that DNA is a special polymer okay so in sense that of course is very important but it's I mean it's a it's a special process it's made of a sequence of of of the chromosomes of g t c and and a and it's and it's very long so it's typical so for instance if you think about the humans so we have a single filament of an a per single chromosome is made of about 100 million bases okay and so this long sequence is wrapped around specific proteins these proteins are called the estons and so then they form so a structure which is called the 10 nanometer fiber so the reason why it's called the 10 nanometer fiber is because the diameter of the compound between DNA and this wrapping is the size of about 10 nanometers and then it was observed that under physiological condition although I mean this part is a bit debated oh well it's actually it's quite debated these 10 nanometer fibers fold into a I mean a coarser fiber if you want and of the diameter which is about 30 nanometer so because of that this folding is called the 30 nanometer fiber okay so then what is I mean what does what does what is exist between the 30 nanometer fiber to the let's say the large scale for the homochromosome is completely unknown so today we know many things about that how it works but we don't know anything we don't have the complete picture so basically all this realm here is needs to be explored and this is where I'm trying to to tell you that where polymer phases can be can be useful at least to say some I mean to predict something and to tell something which possibly isn't on trivia so this is I mean the kind of things that you find in most tech I mean most biological text but what was done I mean during the during the I mean the past years about the work on homochromosome so it was a one I think one of the first important discoveries in the field was realized by these two guys two German scientists Karl Ravel and Todok Borelli who realized that I mean we made a very important discovery in the I mean in the late 50s of the 19th century so notice that was much before that let's say then the discovery of DNA was realized so at that time probably was just a curiosity so what they found they found that chromosomes were not just randomly organized inside the cell but they can be found in specific portions of the nucleus okay and they made so these are pictures of the works I think of Todok Borelli who made the pictures of chromosome inside the nuclei of the center so he really observed and he said that I mean he noticed that these chromosomes are not randomly organized but they obey certain patterns okay so now at the time as I said this was a some kind of a curiosity because I mean the time they didn't know too much about I mean about genetics or about this kind of stuff then much later actually in the 70s I think these these two German scientists actually two brothers Thomas Kramer and Christoph Kramer they made a very clever experiment so what they did they did the following they they have some cells some actually nuclei of some cells and they started they used the lesser beam to destroy the nuclear contact of of these of these cells okay so they beam the chromosomes and then they said so what they made the following hypothesis they said okay if chromosomes I have many chromosomes they look like this way like a spaghetti bowl so then the damage that they create to chromosome should be let's say uh randomly distributed across all the all the all the chromosomes okay I mean because sometimes I let's say I kill the chromosome one I destroy actually chromosome one sometimes chromosome two on average I would destroy all of them in some in some in some pieces and actually but actually it's not what they found they found that damages were really localized to some chromosome and not to the others okay like the the fact that I use the lesser beam I can touch only one chromosome and not the others and so this is only let's say compatible with the hypothesis that chromosomes were localized into a specific portion of the nucleus okay and they should be let's say confined to regions which are smaller than than than the total size of the nucleus okay so that was some kind of direct observation but it came out much I mean more recently always by the same people that used a very clever technique which is called fluorescence and situ hybridization which is a technique that allows you to color I mean to color chromosome each single chromosome inside your favorite cell with some specific probe and then to see it and this is a picture for instance of a chicken fibroblast so each color here identify a single chromosome and this picture shows beautifully that each chromosome is localized to a specific portion of the nucleus so it's not like spread around okay it's it's it's it occupies a specific specific region so imagine that this is sort of the a picture of the world so each chromosome is like a country okay and the the borders between chromosomes are pretty neat with some intermingling between them but otherwise you can really identify a chromosome so now this picture is called this hypothesis this theory let's say it's called the hypothesis of chromosome territoriality today is now is very well accepted and it's it's very general in sense that all let's say superior all organisms provided that the chromosomes are long enough they show territories even humans human minds I mean in mamas this is very difficult let's say and it holds for all cells it's not just like in in a specific cell line it's it holds in all cells because it's a general feature so now it's so general actually they start I mean wondering if it's let's say if it has any biological meaning and the chromosome territories and in fact they show that basically the way chromosomes so chromosomes they form territories but the territories they have also some randomness but actually this randomness is related to how the specific cell line was so for instance they found that in some cells we were chromosomes were found close to the gene so sorry chromosomes were found to close to the cell center and in other cells were found close the same chromosome were found close to the nuclear periphery and this seems to correlate with the functionality of the cell I mean how certain genes are expressed and how certain genes are repressed and in this very beautiful work they finally were able to show that in the same cell line which is the road foster receptors so the distribution of let's say of the chromatin material is inverted in the I mean according to the fact that if the mammal this is the mammal is the urinal let's say is the urinal mammal or is a nocturnal mammal so meaning that the chromosome organization is completely reversed and this according to me it shows that I mean how beautiful somehow evolution works that you have evolution pressure on your chromatin chromosome distribution inside the cells and that also has an implication for the functionality of the specific cell okay so later on I think I'm concluding with a bit with this biological introduction there were other developments in particular probably one of the most probably the most important one of the most important ones is called the chromosome conformational capture so this is a relatively recent technique developed in the lab of Job Decker in the United States and defined by many other groups especially the group of Bingren and University of California San Diego where those people have invented a protocol which allows you to probe chromosome contacts inside the cells why are so important chromatical contacts are important because well people believe that whenever the different chromosomes come into contact they these contacts are related to the fact that some genes are expressed and some genes are expressed okay and so these maps these heat maps here tell you how certain sequences along the genomes interact with the corresponding sequence on the on the same chromosome okay and so now you have all these contact maps are I mean you can find for many many many different organisms they show many features they have many features in common across the organisms but they also display differences and you can quantify these differences and I mean according to these differences you are able also to correlate the let's say the the intensity of this map to specific properties of the genome okay so this is a very important field that let's say that is currently under development I mean strong development and also by studying these maps you can tell something about how chromosomes fold inside the cells I mean how what is their shape or you can reconstruct their shape starting from these from these matrices so now before I mean after this maybe a strong introduction on the on polymers and the chromosome folding problem I tell you if you think how you can use let's say you can use some polymer physics consideration in order to understand how polymers are packed sorry how chromosomes are packed inside the nucleus of the cell okay the first important consideration one has to do is the fact that each so we focus on human cells because it's well it's the ones that are more familiar to us of course and so think that each human cell contains about six times ten to the nine so six about six billion base pair of DNA which so if you stretch them from hand to hand it's about two meters of DNA folded inside each one of our cell okay and this DNA is occupies a very narrow region a region of about 10 microns okay so it's a five order of magnitude less than the total length of the DNA inside the cell okay and so of course I mean this is I mean if you make the proportion this is like putting a rope of 100 about 100 kilometers inside the backpack okay and so the question is how of course I mean this DNA stays inside the nucleus because otherwise we wouldn't work but the question is how you can put all these I mean immense rope inside the narrow space in an efficient manner how it would look like if you if you use a microscope or if you I mean I mean how it should expect that should work I mean inside the such a narrow space so okay this is an astronomical comparison this is the same so if let's say if the nucleus is the earth let's say that it's the same distance of the for DNA like the center of the sun to run so it's I mean it's a huge difference in in landscape so in order to understand the problem or to let's say to be to focus on the problem one so as I said so we have this we have DNA which has all this structure and we have to think a bit I mean how the cell works so you have basically two two stages during the cell cycle and these two stages are one is mitosis and the other is interface so mitosis is the part of the cell cycle where chromosome have this let's say familiar rod like shape in at the end of each mitosis stage the DNA which has this shape of each chromosome started to swell inside the nucleus and occupies its own territory as I said so this is a typical picture of a so this is the nucleus okay and so this is one single chromosome and each color here is one of those okay and so the question is how I mean what it happens here at the end of the code the mitosis of the mitosis when cell enter interface and is it possible to let's say by using oops sorry is it possible to say something here at this point let's say by using let's say simple physical concept so this is basically what motivated me and my collaborator say now a bit slightly more than 10 years ago where we developed a model a polymer physics model computational model in try to somehow understand the formation of chromosome territories now because at the time people well let's say the idea was to use a simple physical model in order to understand a bit the physics of this object and try to also give a possible physical explanation for the presence of for the formation of these territories because you thought maybe since these motifs these territories are spread I mean are general and you can find in all the cells of the organ that should be maybe also a simple physical mechanism that can originate them so what we did basically we did exactly what is here so we simulated the the condensation of chromosomes let's say at the end of the mitosis of mitosis when entering interface in order to do that we constructed let's say model mitotic chromosomes each one is some is basically a big polymer so each one was made of about 30 000 monomer particles each one of these modern particles is this is a normal polymer so there is no sequence information i think it's very simple model let's say it's a it's a kind of model to have in let's say in in any polymer solution any polymer mesh okay we arranged four of this chain in order to keep the simulation doable inside the simulation box with the periodic boundary condition and so we did some as I said we did some coarse graining in the sense that so DNA so we intended to model mammalian cells so each so the typical mammalian genome is the human one each chromosome is very long so you cannot model things let's say at the DNA scale you have to do something coarser but as I said I mean coarse graining is a typical technique that you apply in polymer physics so that thinks maybe it's not so dramatic so just to give you an overview of the scale so here each monomer means that we are modeling a chromosome at a scale which is compatible with 30 nanometer farmers so namely each monomer here is about a three kilo base yes three kilo base pair so it's a it's a coarser model okay and then we use the Brownian dynamics to simulate these these these objects so for those of you who are not familiar with Brownian this basically like numerical integration of let's say of Langevin equation okay so here so for each monomer has some friction Newtonian forces between the monomers plus some plus some noise okay and the noise respects the standard relationship for for for for gush noise so it's very simple and the rational to to use Brownian dynamics is because the chromosome live in a let's say kind of aqueous environment so they are also they also kick they are also and they are also subject to some random noise so this model should work quite okay so if you are if you want these modeling is like saying that chromosomes are a semi-dilute solution of polymer chains okay and the interaction we used to model so the Newtonian interaction between the monomers are simple in sense that they are simple and medium so you have only chain connectivity so basically two monomers which are closed along the chain cannot cannot be separated so you have some stiffness between the I mean along the chain in order to well to cope some with some biological measurement of of chromosomes and then you have to do some mapping in order to model to model with real let's say to map this into real biological problem so the the the sides of the simulation box which is in such a way that the DNA our I mean the density of our polymer is compatible with the natural DNA density and then this is a very important ingredient you have hard core repulsion between monomers namely this means that whenever this thing during the course of simulation I mean each monomer encounter another monomer in his let's say random displacement cannot cross each other I will pump and then we'll we'll go back okay so this is a actually this is a very important ingredient so if you apply that and you you let the simulation go you at the end of the simulation you end up with something like this so the your chains open I mean and after some random displacement they get stuck into some of this conformation okay and this conformation so I've used different color for each polymer actually the result is that they strongly resemble territories in sense that they also occupy specific region of the let's say of the cell of the simulation cell without mixing without liking to mixing with the other with the other with the other polymer and so because you have done molecular dynamic simulation you can attract also the let's say the mean square displacement the random mean square displacement of each one of these bead and you can compare to the experimental results so this was a comparison between our simulation and let's say experiments on the mean square displacement of real genomic loci this allows you to basically to fix the let's say the diffusion coefficient of your simulation I will tell you a bit now I don't have the time to really spend this but I will tell you a bit more details if you're interested this during this question now it's our session this afternoon but I want to just give you an overview of what you can measure because this is quite important so you can now compare the structure of your chains of your similarity chain to experiments for chromosome and here I'm going to give a bit more detail on this so the lines here corresponds to mean square and 20 distances between genomic loci on the simulated fibers this one and symbols refer to the same quantity mean square and 20 distances between genomic loci but now on experiments so real chromosomes okay and the different colors here are referred to different organisms this is the red ones are on refer to east the while this so this is human this is human too and this is a fruit fly the drosophila melanogaster I mean the typical the common fruit fly and what you can see here is that the simulation this simulation although they are somehow relatively simple they are able to reproduce the let's say the average they are able to reproduce the the average conformational chromosome that we're really measuring inside the cell so you can somehow probe the typical structure of of chromosome inside the cells another important observation that you can ask how frequently chromosomes interact in fact that you can measure how out the let's say the the the mean contact frequency between the two loci on the same chromosome decays as a function of the genomic separation between them so there is a consensus now that provided the chromosomes are big enough this law has to be as to decay roughly as one over L huh so this is related to a particular structure of the chromosomes and we found that our sorry the model is able to reproduce indeed these these features so somehow although it's very simple this kind of coarse grain computer simulation is able to capture the average behavior of chromosome in many different conditions for many different organs okay so of course this not all of it I mean there are other features that that should be understood but at least now with this model you can somehow understand detail something about the physics of the process that leave that gives birth to these chromosomes territories and maybe I think I will yeah just tell you about a few things about this so as I said to you so here to to to formulate this model we use the very um so basically no more is this based on a normal polymer structure of course I mean you can object think that okay but chromosomes for sure are not homopolymers because and there are I mean you have DNA sequence and so on and so forth you have many proteins going around in nucleus now because this is perfectly true you are right and so you can ask what it happens if I introduce noise in my model in sense that I I use models I mean together models with the different resolution in sense that some portion of my fiber are more condensed and some portion are less condensed that was that we did a few years later and we saw that so I'm going a bit faster here we saw that basically the model shows some stability in sense that on the larger scale nothing really happens what it happens it really happens here on the small scale and and this of course I mean it's quite important in sense that we interpret that as a sort of stability of the chromosomes and also stability of the model so we have something that works really well on some scale but I mean on large scale if on small scale something changes this is of course perfectly acceptable but then the overall structure remains stable and since I think my time is a bit over so I prefer to leave a few minutes for questions I will well I leave this this consideration out because a bit maybe a bit more advanced but I'm happy to answer your question if you have if I'm more curious about that I just want to finish by acknowledging two people that work with me on this on this I mean on this chromosome story first of all Rath Evers which with whom we started this work together many years ago now more than 10 years ago and Ana Maria Floresco was a postdoc with me in CISA and together with her we developed this mixed fiber model for for chromosome and of course since this is a numerical workshop it's important to acknowledge HPC resources because these simulations are quite intensive so in particular the TSM in Lyon and in China in Italy and also the our local CISA cluster here in CISA and with that I think I'm done so I'm happy to take questions so if you want to ask a question you can I guess unmute yourself and go ahead can you hear me okay good hello Angelou thanks for the talk I was wondering is it possible to model a change of methylation on the distance a change of methylation yes so it depends what you so you want to somehow change the state let's say of your monomer somehow yes I would like to write yes I understand that you you don't model the distance specifically so yes no yes it's a very good question thanks for it yes so there are actually there are already many a lot of work on that so I remember at least two groups now maybe there are more so there are there are there for sure there is work from the from the group of Edimbra of Davide Marenduzzo I don't know if you know him so Davide has done a lot of work on that where they basically they assign a specific state to to each monomer let's say up and down where you have a particular state of methylation and you call state up and in particular another state of methylation down so it's a sort of spin system okay and this change dynamically in the course of the simulation and in particular it's related to when these two spins for instance come together they are allowed to change in order to see the spreading of the methylation on the chromosome otherwise there is also a work so this is an approach and also there is a work from the group of Andrew Spackowitz in so it's it's in California I think it's Caltech yes and so basically what they did they also used polymer model and I think they did not study the spreading of methylation but what they study they study so they assume that somehow methylation is fixed and they study what's what's the consequence of some specific proteins that attaches to the let's say to the metadata states of the chromosome and they see the consequence on the chromosome conformation okay so in the end yes that can be done of course there are certain assumptions because then you have to let's say you have to to I would say you have to assume how this thing's changing so in the end the idea is that you formulate this simple assumption you see that for instance if you can reproduce the methylation patterns of your specific cell because of course they also change from cell line to cell line okay so but in the end yeah in principle it can be done yes I don't know if I if I answer the question sure yeah about the first approach you mentioned is it like an icing model it's like an icing model or even a pot model because maybe it depends on how many states you assign okay then it's a bit of course that's relatively easy to change so then what it's important the kind of rules you assign in order to change the state in general what they do if I remember correct is that whenever two monomers come close to each other in space either because they are close in space because they are close in sequence or because they're close in space because just because of the random fluctuation of the fiber you are allowed to change the to transmit or if you want the methylation state of the event and then yeah this kind of thing because I mean this fiber is very long but then even if it's long because we have a polymer can come close to each other just because of the random clash but in principle it can be done yes cool thank you okay I guess well there'll be time for more Q&A in the afternoon so thank you very much Angelo