 so thank you very much so I will present some results that we have with about the statistical properties of DNA in various it again yeah this one yeah okay thank you yeah so otherwise the moon just shakes like this okay so thank you very much to the organizer and yeah it's coming so thank you and all the people here so I'm sorry that I could not follow the first three days of this conference with I suppose beautiful talks and and so I will present what we did on DNA and so first for a physicist why DNA and why it is interesting for polymer physics you see here three possible way of seeing the DNA and three different parameters one is a length scale one is the elastic properties so the young models and one is the temperature so you could find DNA in this shape here if it is very short so if it is shorter much shorter than the persistence length or if the DNA is made up of a very very stiff material or if you are looking at DNA at low zero temperature and as you increase the temperature you increase the actually the thermal energy at disposal so the DNA might look something like this or if if the elastic properties are average then it can also look like this or if you are looking DNA on longer length scale than the persistence length then it will look like this and the DNA will look something like this if it is very large or very flexible or if you are at very high temperature and so how to to characterize this all this behavior here it's bound here into the persistence length the persistence length is you can imagine this is the stick that you can use to describe the contour of the DNA and this persistence length is the elastic modules that you see here the temperature there are the three parameters are related with this equation here and where is DNA well DNA is exactly between if we are looking at length scale we can see we can have DNA between one and maybe 100 microns so the persistence length is 50 nanometers so we can study the DNA for values of length scales which are smaller much smaller than the persistence length and scales that are much much larger the elastic properties are just something also between very hard material and very soft material is 10 to the eighth Pascal and the temperature of course we cannot change it too much is something like the 300 Kelvin so it's a very interesting polymer for doing polymer physics because you can go study it from the very stiff behavior to the average to the semi-flexible behavior to the very flexible behavior and what is interesting for the physics point of view polymers are just one kind of second order phase transitions that you see and are characterized by the two important parameters the dimension of the space in which they are embedded and the dimension of the order parameter in this case is n equal 3 and whatever equals 0 n equals 0 d equal 3 and this was identified by the gen to describe polymer and what polymer physicists do is actually to test scaling law like this one so the size of the polymer should scale with the length to some kind of exponent and this exponent will depend upon the upon the dimension of the space so I will write it this here just to you know to do like the big physicists that were in this room here so I have also the honor to write on the same table that Abdul Salam was writing you know so okay so so then there is topology this is why why DNA is interesting for us so we can have DNA in very different topology so we can have it linear circular or not it which makes them very interesting to study and so when you are looking at DNA so DNA is actually two curves which are linked together like this is a linear DNA or you can have it you can have it circular like this one so to have a circular topology or if you like also you can have it as a noted as a noted topology so you can have all three possible interesting topology that you can make up with the wire the other stuff which is really interesting for physics is the linking number so it tells you how many times the DNA strands are going around to each other is related to magnetism and here you see biosavar law that allows you to calculate if I give you a current it allows you to calculate around any curve the magnetic field but if you integrate along the green line the magnetic field this is using amperes law then you get this relationship and when you plug the biosavar in here you get out actually the linking number you get out these quantities which is called actually the Gauss integral and you see here if I have two currents loop and I am integrating three times around the electric field this integral it's a equal six and tells me how many times these two curves are linked one to each other the other point is which is interesting so of course cellular division you see it here I show it because often you know physicists never saw in their life a well never saw in their life a cell division and so of course it doesn't work okay and so the this chromosome will you see this big mess here in the in the middle and where the DNA chromosome are duplicated and that they are pulled apart by the the motors and but for doing this I mean you can imagine that there are tons of crossings and so these crossings have to be solved so that you can separate DNA and then we have to rely on the topoisomerase that we were listening to this morning at least from Eric about this so this is an interesting question how to entangle DNA and how topoisomerase for example works and the other very interesting stuff is this the this is the nucleus of a human cell if I'm not wrong and teach chromosome its color tier in a very clever way by biologists biochemists with a different color and teach chromosome it is it is confined into a chromosomal domain so the DNA in the nucleus when it is not during the division is so mixed up in in one single big chunk but each each chromosome is perfectly separated and so how do we understand this from the physical point of view also it's a very interesting problem and when it divides you see the chromosome just coming out so they and then they will go back to this very very compact form and so for in understanding all these kind of problems it's important at least from what we can do as a physicist to see the relationship between the topology between the elastic properties of the DNA and the polymer properties of DNA as an elastic wire and so what we are studying actually are just a small part that the cell uses for for the from the DNA you know the cells uses at the sequence the elastic properties topological properties statistical properties and many many many other properties in order to properly function but what we are studying in my laboratory are just this limited to these three points here that I will speak about so how do we do this well we take DNA we imagine this by atomic force microscope and then we we trace the DNA and then we can calculate all the properties that you want to study using this data so this is the typical experiments we take a DNA we put it on a on a very flat surface like you see here this is an a two-dimensional configuration and then we write a sample and then we come with the atomic force microscope that you see here we can do the imaging of the DNA and get the the contour these here you see for a very small for a very small DNA and then we trace it like this with some program and then I'm saying that oh well at this exact point we are as good as any theorist once we have the coordinates of the of the DNA molecule we can calculate any quantities and so this is the the interesting part and what is also interesting is by using the atomic force microscope you don't just get the average value of quantities you get the value for each single molecule that you can then at the end average or you can look at the distribution which is actually an additional information that we can deliver we're using this technique here and so as you know theoretician will just first calculate the what is the distribution for for I don't know a polymer for certain properties of the polymer and then calculate the average value that is measured by the experiments and so we have we are one step a little bit more in detail we can get the distribution and then compare them with the predictions of the of the of of the theory so these are the different topology we are studying and so the the position of of the DNA on the surface is two-dimensional because the attraction is is weak and and as you can see here the DNA then goes down it is in the pure actually two-dimensional two-dimensional configuration here you see molecules which are imaging in solution and you see that they can really move on on the surface you see here we just by a trick we had an intercalant and then the DNA just supercoiled positively supercoiled on itself and so it the function or the idea of this experiment is to show that actually DNA is can move around on the surface and and it can be you know there can be some you know interaction with proteins and stuff like this so it's really alive on the surface and then when we dry it then it will be it will be just it will just take the conformation that it has so it can relax into dimension so we what we go to what we want to do is of course to look at this at this scaling law so how do we do so we take the trace molecule you see here a linear molecule we choose in this molecule a given contour length like you see here in green and then we calculate the end-to-end distance and we do it this for many many position on the on the molecule and we get out for a given contour line we get out the average end-to-end distance and then we plot this in a double logarithmic scale as you can see here just to test the power loss and then we can get out as you can see here the critical exponents for for the end-to-end distance as a function of the length of the molecule the other quantities that we can actually study is the radius of duration that it will also scale like the like the length of of them of the molecule or what we can also do is to study the the directional correlation function along the molecule so if you take this vector here and the same tangent vector at the distance s what we are looking is the angle the average angle that they will do and so if the molecule is stiff this angle it will be zero is it flexible the average would be just whatever it is it will be zero and and and this function decays exponentially with the with distance along the molecule and and the and the decay constant is just a persistent length from this we get out actually the elastic properties of the DNA by by by fitting this function so this is the other quantity that that that we can determine from the from the experiments and then the third information or the fourth information we can get is just the shape parameters since we are looking at the single molecule so we can get out shape parameters like you can see here just the as ferricity which is you know if we if we just fit if we fit a ellipse along the DNA with a molecule we are looking the as ferricity tell us if the molecule is more elongated or circular so the as ferricity is something like that the the big axis of the of of the ellipse over the the sum of two of the two so if the molecule is circular the the as ferricity is just zero if it is long getting like this it will be one and on the opposite the anisotropy is just the minor axis over the larger axis and this is exactly the opposite and something like this and these are shape parameter that we can determine from from our data let's just look now at some data are some Polish guy or okay so maybe okay sorry I like the moon but not that far so okay so and so here now so this is DNA now a circular DNA which is Nick so it is relax it has no super calling of different length and you see already what is happening when it is very short it adopts a circular behavior just like a circle and as it get longer and longer it looks more and more flexible but actually the properties doesn't change it's always the same temperature it's always the same elastic modulus it's just that what I was telling you if you are looking DNA on very short length scale it looks different you're looking at very long length scale it will look it will look flexible and the same if you take a train track and you are looking the train tracking in in Trieste it looks like this and you are in Paris it will look like this and so I on short length scale it's absolutely stiff you could never imagine that you take a truck and then bend it up up to Paris and this is exactly what is happening here so just a question of length scales in this case and so for this molecule we just determined the the the radius of generation and and and plotted against the length of the plasmid and you see these are the data point and what you can see exactly here at the beginning you know the slope it's one telling us that the the system it is one dimensional because it's stiff and then as as we cross the the persistence length then it gets like a flexible two-dimensional polymer and and the exponent it is just 0.75 as the theory tell us so this is exactly the behavior we can also study the end-to-end distance of course the molecule is circular so it has a shape like this as we plot it as a function of the contour line here you see for very short DNA up to the longest one so six micrometers that we have and then we can fit it with this formula that is from 1949 so exactly 67 years ago and and was never experimentally verified and here we can verify this formula we can get out the critical exponent here and we see that as the DNA gets longer and longer you see that the critical exponent goes about from 1 down to 75 as we expect for for this kind of stuff and then you can use for example scaling you see perfect perfect overlap the other quantity is of course the bond bond correlation function here you see what one of this function for a short DNA you see that for circular DNA it is symmetric because when you are halfway along the molecule the two vector are perfectly opposite correlated so completely negative correlation and then it goes back of course to positive correlation this is for a short DNA and then you can try to fit this for example with the correlation function of a circle is not really possible because this DNA is still a little bit flexible and so there is kind of of course not perfectly anti-correlation here because the DNA is flexible and this is the effect that you can see that when you are using some flexible DNA you can fit perfectly this correlation function for short DNA may now for all the DNAs you see here the raw data you see that this correlation function first decays exponentially as I was telling to you with this form here but then the circularity comes in and it has to be anti-correlated so it gets negative in contrast to what this formula says and then it goes back to the to one again and what is interesting you see here that as the DNA get longer and longer so these are the short DNA and then gets longer and longer the anti-correlation at midway along the molecule decreases because it is flexible so you have the one vector here the other here if it's stiff these are perfectly anti- correlated if it's long it's flexible and so this anti-correlation just decreases and then Sakawe and Irofumi Wada just did theoretical work on it just to interpret and calculate this correlation function and you see here that there is a nice overlap between our data for for a two micron DNA and their theory and so and in this case they take into account the fact that if the DNA it isn't into dimension there is interaction between the strands here and this influences actually the correlation function for this kind of DNA so the other stuff is that we can do is the shape parameter so you see here short DNA and longer DNA so that the DNA was just taken and then rotated to have the major axis all in the same direction so that the molecule are all oriented and you see that if it is short then there is a hole because the DNA cannot cannot fluke to it it is stiff but as it gets longer and longer of course this is just filling this this gap here and so the shape of the DNA goes from saying from almost circular to something that is more elongated and this shape was the studied together with Erwin Frey in in in Munich and and you can see here their simulation you know for a self-avoiding circular DNA and somewhere are our points that really stay on the line and so again we can say that DNA is a self-avoiding walk and that the interactions when we are in two dimensions that takes place inside here and determine influences that the shape the other question we were discussing and just mentioning is the fact that DNA it is actually in a very very crowded environment and so we went up to study DNA in high concentration so this is the diluted case and this is the case where we put down a circular DNA of 1400 nanometers about in very concentrated solution and you can see that here the shape are really interesting but but when it is concentrated with some animals appearing inside here and these are just due to to the fact that the DNA which is around just make a pressure on the molecule which is in in in the solution so to speak and so we actually with one sample we have three different type of confined geometries one geometry is this one when the molecule is confined by the other flexible molecule around and then we have the geometry that you probably somewhere you see a molecule inside another one we have the geometry of a molecule which is inside the kind of of circular confinement and then we have the one which is outside that feels the pressure from the inside and so we have three different kind of of geometries that can be studied with one with one sample and here you see the the case for example for for the molecule which is inside which adopts a shape which is a cross cross on light because this seems to be the one that is more probable the one that has a lower energy and then we we took all these molecules and then calculated for example that bonbon correlation function and then you see here we have a still another type of bonbon correlation function it decays of course at the beginning exponential because the molecule is just fluctuating but then it comes up again around the halfway because the molecule goes around with this shape and this makes that the correlation function comes up again slightly positive at midway and then the PhD student G. Ohm just did some simulation to to calculate this numerically this function and then he could show that if it puts around the perfect circular molecule then he can explain exactly what we measure but this is just what we find out so we have some now hints how DNA molecule behave in in concentrated solution of course unfortunately is only in two-dimension and and and the DNA is actually in three dimensions but what Sakawe did after the work he did with us is that what what he understood and on two-dimension it could then extend his theory in three-dimension which is now a theory that awaits of course awaits of course confirmation by experiments but this is the way we we can work okay and of course also when you are looking at the bonbon correlation function you see this effect that if the molecule is is flexible the persistence length is is shorter and then the decay is much faster so so if you have the concentrated molecule which is inside here it looks more flexible but it is not more flexible from the point of view of of the elastic modulus is just but the fact that by the pressure this makes look the molecule more flexible and if you are looking the molecule which is outside this molecule looks more stiffer because it just have the internal pressure and then the decay function the correlation function decays much slower because the effective persistence lengthy is higher the same stuff you can see it with the end-to-end distance you see here the reference DNA circular D in dilute solution and then if you are looking inside the one molecule so that the of course the end-to-end distance has to to become shorter because the molecule is pressed if you look at the molecule which is confined by the other molecule will be the green line here and if you are looking to the molecule which are swollen so the black one here then it is much larger and what we can do of course and this is the interesting part is because the polymer in concentrated solution behave like gaussian gaussian curves and and and and and this means that the critical exponent is point five and so we go from when it is in dilute solution we go from point seventy five which is a self-avoiding prediction here and we go you see in in concentrated solution we go toward point five six we cannot push it down more because it's really difficult to to to get a concentrated solutions on the surface so we try desperately but you know if DNA doesn't want then it doesn't want of course okay then of course I was inspired by the experiment by Davide so who is down there up there you know so he's now become a master for me this kind of experiments macroscopic mac experiments where he was studying the effect of of of concentrated solution of circular polymers by using sparsely in in this way you know and this is the three-dimensional case that we actually would like to do with DNA but it's not possible and so I thought to redo the experiments at home you know but I wanted to do a blind experiments you know I didn't want to tell to the person who was eating what what we I expect or what I am studying yes yeah yeah yeah yeah I mean the if you are taking a linear DNA in concentrated solution new is equal of course in two dimensions it looks like if you feel the plan then you have the you know the you have the fractal dimension of two and you have new equal one half of course in a two-dimensional is trivial and my experiment is trivial okay so this is the essence so so this we should do of course three-dimensional experiments these were done of course in 1985 or 86 the gendered with his group some experiment using Newton scattering in concentrated linear DNA and and and this was famous experiment is a beautiful paper in macromolecules using the deuterated linear chains of DNA of polymer polystyrene diluted in a in a sea of undeterrated and it could of course study exactly this but of course he got the Nobel Prize and I I got the IG Nobel you know so with Andre we were nominated you know for the spaghetti experiment the one or not you know so we didn't get it unfortunately so it was a big deception okay so inspired by this so what I did I prepared this pasta and then I gave it to my son you know but he was very very cautious to eat but now you see the effect of the entangle so he is well educated but he's you see that the circular DNA you get a bunch of DNA coming up because the because the past it is really entangled you know and he's very hungry and and sometimes it goes better you know and sometimes you you get really huge quantities of course and wasn't not too good way of doing it so some of them were just breaking so took me a lot of time to convince him to eat it because he was really fearing I was trying to do some joke on him you know but you know so okay so now the best way of doing of course effect of confinement it would be if also you could actually have a well-defined geometry to do this experiment so with with Christian and then so we started some experiment and Sandro Giapparizzi my PhD was doing the actual experiment so if you are taking the positive like I we are doing DNA on a surface in two-dimension so it will just be a squeeze down in two-dimension there is no effect of actually of confinement because it's in two-dimension and so the DNA we just spread out something like this and you can explain exactly how it behave if you take kind of like bubble bubble theory and then so okay nothing special but if you are confining it for example exactly in in one some kind of one-dimensional as lead then of course we will see some changes so if the the size of the slit is much bigger than the persistence length then if the DNA is short it will be circular if it is long it will be looking like this and and and and an isotropy it will be 0.29 so which is expected if of course the slit is smaller comparable to the persistence length or to some size of the polymer if it's short of course it's still circular the anisotropy is one but as it gets bigger and bigger you expect a decrease in into the anisotropy to 0.2 and so we did some experiments about this by using slit and then putting this on on the surface and and let DNA go inside these lids on the on our sample holder so to speak and then afterwards we take away everything we dry the the the the sample and then we study the molecules that are that were inside the the slit something like this and here you see some examples of DNA of different length this is outside the slit and as it gets inside these are 10 microns lids so these are much much bigger than the than the size of the of the molecule and these are 600 nanometers which has lids which are about the size of the of the of the DNA and so the the the summary of this is not a joke but you have just to look at two at two points here so if if that this is a long DNA which is 8.5 kilo base pairs which has a ratio of generation of something of 250 nanometers if it is outside so if it is without constraint the anisotropy you see it's 0.29 as expected from theory and as you go inside small slits then you see that is decreasing so we see this effect of the molecule getting elongated of course we should do it awesome with much longer DNA but the problem DNA don't want to get in there so I'm trying to do some experiments to get more DNA inside longer DNA but it's really difficult of course there are experiments that are done using using optical methods which allows to to do the confinement very well but then the resolution is much less because you have the resolution of the optical microscope and so you have maybe I don't know 500 nanometers something like this instead here we have a very high resolution so we could get very very detailed information actually about how the DNA behaves but the of course the disadvantage is that at the moment we cannot really go more into into this problem and then with Enzo and Christian or Christian and Enzo these are the experimental curves and and these are the simulated curve and so we see so the black curve is the control the red one it is the big slits and the blue one is the small slits so you see some changes of the bonbon correlation function here exactly at half way along the molecule and with their simulation they could explain this curve here and the effect so it looks like the molecule because it is of course into the slit there is more correlation between between the between the the tangent vector so if you have a molecule like this of course this one it is more anti correlated with this guy halfway or or with the other one but if the molecule it is flexible like this well there is less anti correlation you know and so this can be seen here in into this experiment and with the with the simulation so now what did we also discovered by doing this kind of experiment is that when we these were nicked molecules because we don't want to have supercalling coming coming in and complicated the problem and what we saw that when when we are inside the slit we saw this airpin forming here and along the molecule this kind of effect when the molecule are inside and we could show with Sandro that this the number of airpin just correspond to the number of of nicking site on the molecule and we could do the experiment need come purpose the molecule and then see that this kind of nicking appears and this is from I think I hope for the biological point of view it's an interesting information it means that when DNA it is in concentrated solution nicking site are in this conformation and then of course this will prevent the reading of the DNA by this site so one question that we have is this used by the cell to to control for example gene genes to regulate genes you introduce a nick you stop the transcription you take it away well you have it again free so this could be one mechanism of controlling gene but of course maybe the biologist here for example Lynn might oh no she says oh no don't come with this theory you know calling yes but you know if you have much longer DNA then then because of the constraints that you can sustain still supercoiling you know and have nicks I don't know maybe okay okay the the other stuff I would like to show you is is the the fact that if you want to to to transcript and read DNA you have to open the DNA so that you get access to to the starting point of the of the gene and reading the DNA but of course DNA the natures at 70 degrees C so at room temperature or 37 degree our DNA will never open so it will never be transcribed will never be and we will be dead you know so so so nature did a mistake in this case you know because life is at 37 degrees and DNA doesn't open doesn't open so how how the nature solve this problem is is to introduce actually supercoiling and so if we are taking a supercoil a supercoil DNA means that this before closing the DNA the enzymes take away actually twist so it it has a linking number which is smaller than the natural linking number that would be given just for the from the twist you know and so if you are taking a molecule closet it so you can this is the the ideal form with eight actually a link of eight but before closing it you take away one turn and then you have an under one the DNA molecule and but molecule is not happy because the you know there is torsion on the molecule and so how the distortion is relaxed it is by using the the color color going around whatever theorem you know from 1959 I was published in French in a Romanian journal something like this and and so it has the choice to relax this this torsion into into bending by increasing the the right so so making the right actually negative or the other way is to open a bubble you know so you can open a bubble like this and so the rest of the DNA is happy and you have a bubble and so in this way you you can actually open DNA and this is why actually DNA it's negatively super quiet it is under one so that the probability to open is just increased and so the opening temperature actually goes from 70 degrees down to 37 or whatever it is needed of course there are tons of proteins tons of whatever phenomena that allows the cell to open the beginning of the gene and stuff like this this is just one physical part but of course there are tons of other stuff which are you know also playing a role just to show you this we are taking negatively coil supercoil DNA here we add an intercalant so we change the twist the linking number is constant we change the twist and the right goes then as we add the intercalant the right goes from negative goes to zero in this case here is the same DNA just with the intercalant we are just changing the twist from here to here we are just actually you know lowering the twist and so the the the the the right has to go up and as we add more and more then the the DNA gets a positively supercoil in this case so do you see this effect and the consequence of actually under winding DNA is that bubbles can open so you can test yourself you take a rope multi filament rope you're just turning against the you know the helical structure of the rope and then you can have open DNA and so what we did with the positive DNA on the surface and then we will look at at this DNA and we saw that there are actually bubbles that open into into the DNA and so what we did we correlated the length of this of this bubble with actually the right of of the molecule so and the right is just given by the number of crossing that it has if it has a lot of crossings that the right is is is large is negative and so the the the twist can be can be again to the standard value if the right is lower then the molecule relaxes the stress by opening that the bubble and then we take the the actual bubble size here as a function of the remaining crossings so these are molecule with a little you know little right and the bubble is big until your molecule a molecule which a higher right and a smaller bubble and what you see here the red line is the red line by taking account only topological topological values it means twist and right and the linking number and and the bubble size is smaller of about 12.5 nanometers in this case here on now for all of this and this is just due to the fact that part of the stress of the molecule can be relaxing to the torsional of the DNA and so Ralph Metzer just did a theory about it this part is here is just geometry topology so this is the red line and this part here is 12.5 nanometers and the parameters that there are here are just parameter that we got from from the literature people measuring the torsional module of the DNA people that measure the the the in principle the the the some yeah this is the length of the of for example a single stranded DNA double stranded DNA and so on so forth and this give you exactly 12 nanometers so there are no we we didn't choose any parameter just put it in there and the theoretical goes straight to to our data okay so but of course for opening you have to introduce into the into the bubble into the DNA some weak point so if you want to break something just put a weak point in there and then you can break it so and and DNA does it like this by taking by taking a series of weak base pairs so that it will open at a given place because if you're putting torsion of the molecule it can open anywhere but you don't want to open anywhere so you need the place where there is a weak point and so this is done like this and you can see here we just took the same DNA as before we just dimerized it so we have two of them and you see that there are two bubbles in there so probably at this place here there there is a lot of TATAT sequence so that is weak and then it will open exactly at this place here okay so this is what we we we we can do and so how how does the then the cell react as the temperature goes up since if you increase the thermal energy you will increase the the opening probability and and how it is reacting well is reacting by reducing the the delta Lk and here you see some measurement we did on E. coli and the DNA from E. coli we grew DNA the bacteria at different temperature and then measure the the the super helical density and you see this is negative the super helical density and as we increase the temperature this goes down because DNA opens here more easily because of the higher temperature than here so you need less under winding to open the open DNA and so you have the confirmation here and now there is just something for adorati which is just there in the back she was showing these beautiful images of minimal surfaces some nuts so I have one here for you this is a 4-1 nut with a sub-bubble in there and so you see the the the surface here and then in in the center here there is a tetrahedral structure you know so where the you know the the four the four surfaces meet if you're doing this with a three-foil nut you will have just three three lines coming and then I could not go up higher to do the experiment but so you know I did the experiment you do the theory and we get married and we'll be happy oh no sorry sorry sorry okay so this is for thanking the people that were working on this project and thank you for your attention