 colloquium on quantitative life sciences, which we are organizing jointly between ICTP QLS section and IET Mumbai. As we said in previous editions, this is a very open talk on active matter dedicated to general public and students. So, I remind the audience that the speaker is happy to reply to questions, especially if they are short during his talk. If you have more technical questions, you can keep them for the end of the seminar. He also announced that in the middle of the there will be a break halfway of the talk, because he will present two topics, you can also ask questions about the first topic in this break. And with no more delays, I give my word to my colleagues from Mumbai who will introduce the speaker. Thank you, Edgar. So it is my pleasure to welcome Professor Garhad Gomber to the monthly colloquium jointly organized by ICTP and IET Bombay. And it is diploma and PhD in physics at Ludwig Maximilian University in Ulish. I'm sorry in Munich. He did his postdoctoral work at the University of Seattle. And after the postdoctoral work from 1994 to 1999, Professor Gomber was a scientist at Max Planck Institute for colloids and interfaces. At that time it was in Berlin. And from 99 onwards, Professor Gomber is a director of the Division of Theoretical Soft Matter and Biophysics at the Institute of Complex Systems and Institute of Advanced Simulations at Forsen Center in Ulish. And from 2000 onwards is a full professor at University of Cologne. Professor Gomber's group has made many significant contributions to the study of non-equilibrium dynamics of many soft matter systems, including polymers, membranes, vesicles, red blood cells and active cell propelling particles. The group has pioneered and developed many computational tools, especially to study the hydrodynamic nature of such the dynamics of soft matter systems, and which has been widely used today. Today we'll be talking about computational physics of active filaments and membranes and cells. Without further ado, I welcome Professor Gomber to start the colloquium. Thank you. Thanks to both of you for the nice introduction. Mr. Gyulich in Munich is not uncommon. Many people may say what was in Munich. Okay, let me start. So I want to tell you something about the physics of active filaments, membranes and cells today. Let me start. Sorry, I think there was one speaker who had the microphone on, but the problem is solved. I think go ahead please unmute once. I mean the problem is with this laser point that also has to switch back and forth, but no problem. Well, I just want to give you a couple of examples for active matter in biological systems also in synthetic systems. And so let me start with a cytoskeleton. Like you see here a movie which you don't see. Okay, guys, so I have to switch from the laser pointed to this arrow because otherwise I cannot operate the movies and so on. All right, so the first is this cytoskeleton and there's this interesting phenomenon of cytoplasmic streaming. Come on. Yeah, no. Yeah, so you see here this is driven. This is in a driven by the cytoskeleton network in a microtubule of microtubules in the dosophila site and the mechanism you can see here on the left. So the two microtubules or any two microtubules which are connected by kinesin motors are pushed relative to each other and that sets into motion this whole network. But this is can be studied more easily. Such phenomena can be studied more easily in motility essays where motor proteins in this case it's myosin and acting. Anchored on the cover slip. It grabs on acting filaments which are on top and then pushes them forward. So this is a system which can be studied much more easily in the lab. Another example is motile bacteria and I don't I'm not really quite sure about the mechanism which by which they operate maybe this is a bit. Complication is still needs to be clarified, but the behavior is quite spectacular if you as you can see here. This is only the motion of single particles as you saw from the site is cosmic streaming, but many of this bacteria interact and contribute to their relative motion. And the last thing I want to show is cell motility sorry this is not a movie. This is crawling carousel site on the substrate, and it's moving in the in the B direction. This is a characteristic shape signal like shape and it's moving forward quite persistently. Yeah, so in in all these system which I've shown you, I think the important point which I want to focus on today is this interplay of propulsion and deformation yeah you have you have seen this here the shape is not not circle. I mean, and this is only during the motion and also if you think of the bacteria before that they are strongly deforming because of the propulsion. All right so in the first part of my talk I want to tell you something about this active filaments. There are different ways of propelling a filament. I want to focus on one particular case, which is tangential propulsion. Yeah, so you have this filament which you see here on at each point. So if you think of a discretized chain and on each of the beats which make up the change there's a propulsion force and the propulsion forces always in the tangential direction of the filament. This really has a polarity. So in this case it's moving from the light gray side to the dark gray side. So if you went to model such an object, you can just take your favorite polymer model. I mean we use be spring warm like chain model. Also talk about the several filament that we will also see that already for a single filament excluded volume can be important and this is done by overlapping the Jones potential week week. So this is an exchange the Anderson potentials which are purely repulsive. And then I mentioned that this is active tangential driving force, and essentially everything I've say today, there will be no hydrodynamic interaction included so it's essentially a brown in all our brown in dynamic simulations. And then if you think of this problem, then you can define a couple of dimensionless numbers, but one is the persistence length, which is bending maturity over kt divided by the filament length. So that means if if this person's dimensionless persistence length is larger than one that means it's rather stiff object if it's less than one that is quite flexible. Then we have the pickling number with this the velocity times the length of the object divided by the translational diffusion coefficient, and you can also translate this into a propulsion force times length scale squared over kt. And then we have the flexion number which is measures is a ratio it's it's not a new number it's it's the ratio of pickling number and persistence length, but still it's sometimes interesting to see because it tends to tells you the balance between curvature energy curvature forces and propulsion forces. Right, so if you throw this thing then into a two dimensional box and right, so this is this flexible filaments. The bullets here are just markers there are no obstacles so they're just that you can see the motion of the filament more clearly. You so you you see it moves, of course, in this particular case, the presence length is rather small so therefore it's strongly fluctuating. And you can also see indications that there's a tendency for spiral formation and that's why we're the excluded volume interaction actually comes into play. Now, if you do this and look at this in a bit more detail as a function of some parameters and I will tell you about the parameters in a minute, then we can distinguish two or three different behaviors. Right, so the first behavior is what is shown here in a body what I call the polymer regime, and you can see the conformations of the polymer of this filament here in the insets, and what the red is the trajectory of the center of mass. Yeah, so you see it's kind of a random walk like motion and the conformations at each moment that look pretty much like a semi flexible polymer. Yeah, then there's this intermediate regime which we call only I still first go to the right hand side the strong strong spiral regime, and you just look here and this little insight, you see sometimes the polymer winds up in a in a very tight spiral. Yeah, this and you can see this also in the trajectory. This is when there's hardly any motion, you have only some local diffusion, and then the polymer is extended again it moves forward. Ballistically, well almost ballistically persistently, then it spirals up again moves again and so on. And there's the regime in between which we call the mixed spiral regime, just the number of spirals is spiraling events is this less frequent. All right, now, look at this in a little bit more detail. And one of the interesting aspects before we found is that there is an enhanced rotational diffusion. Yeah, what is plotted here is the rotational diffusion coefficient of the whole chain. Yeah, given by the, I will explain this in the next transparency, given by the end to end vector of the chain, as it rotates, and this is shown. This is shown here as a function of the flexion number. And you see that there is there's very little rotational diffusion just a passive rotational diffusion for small activity. And then, when the activity becomes bigger, there seems to be a kind of universal behavior, because the all the data for a very different persistence length, all fall onto a single line and this is single line has slow what. And the diffusion increases linearly with with activity. So how we can we understand this, this behavior, and this is a little theory it's about the almost trivial theory. So we look at the end to end vector te as a function of time related to the tension vector at earlier time zero. And that decays exponentially with this rotational diffusion coefficient that's just the definition of our rotational diffusion coefficient. Yeah, then, if you want, then we have this linear increase reflection number I explained this to you. So now our little theory. Yeah, let's assume we have a railway type motion of the filament that is the filament is has the the same is like a section of a very long polymer chain, which has this is just an equilibrium confirmation. Yeah, so think of a very long, infinite long polymer. And the polymer be looking at the motion is just the motion that long of a little segment along this railway given by the infinity long polymer. So the infinite long polymer we know what the tension tension vector correlation is, let's say it's passive at the moment so for the stars so velocity is zero, which means it's not not time dependent and then the correlation function t of s t of s prime is just an exponential decay, exponent of s minus s prime, divided by the persistence length. And if we are thinking of this, our little polymer moving just as a part of a long polymer, then that just means the position s changes as prime is unchanged and s becomes s minus or plus velocity times t. So that's the motion along the chain. So if you use this relation and just say okay the for the end to end vector of course we have to integrate the tension vector over s from zero to L similar over s prime from zero to L, which is very easy calculation it's just an exponential Then we get again an exponential decay as predicted here, and the result is rotational diffusion coefficient is the driving velocity divided by the persistence length, which is exactly this linear universal linear behavior, which we see here where universal of course comes because we divide here by the persistence length for different persistence length. So I hope that gives you a feeling where this enhanced rotational diffusion comes from. Now if you look at kind of a phase diagram of persistence length versus Peckley number, then I think this is not too surprising that we see the spiral regime. And the persistence length is high, strong will function, and the persist that sorry the when the Peckley number is high and the persistence length is low, because if the persistence length is low. Then it's easy for the, for the front part of the chain to have a high curvature and hit the tail and thereby start the spiraling. The persistence length is high in the Peckley number is low, we are in the polymer regime because the polymer behaves more like a passive, passive polymer. And the boundary between the two is this green green line, and this is roughly given by persistent length proportional to Peckley number. This will occur again and again in this what I'm telling you afterwards and I think that it's relatively easy to understand, but because we need a propulsion strength, a propulsion force, which is comparable to the bending strength, the bending forces. And since the bending forces are given by the persist by the bending rigidity or the persistence thing. I think this is a natural result to expect bending forces and propulsion forces are similar. And then you see that transition between the two, if persistence dominates activity plays a little role if persistence dominates, then this is dominating and leads to this highly non equilibrium kind of behavior. But it's also shown here this purple region. This is the primary parameter space for acting filaments on this myosin carpets for this motility assays. So we would claim that it would be possible to see this transition from polymer to strong to spiraling in these motility assays. All right. So for a single filament. Now let's look at what happens if the concentration increases. Yeah, I mean this we are talking here still at a very small concentration should be set here somewhere. Okay, it's on the order 0.01 or point. Okay, I can't see it now. The pictures are on the way. No. Okay, this is at a relatively small concentration in any case. So, let me just play the movie. Maybe I start with a movie here at the bottom. This is very short filaments. And this is actually a behavior we have not really fully understood the dependence of the spiraling on the on the length of the filament. And so you hear small filaments shown some spiraling, but not much spiraling longer filament show much stronger spiraling. And I think the reason is if you have the width of the chain, the also plays a role, because if you think of a short chain, you can only wind it, say two times around itself, then the length is exhausted. If you have a very long polymer you of course you can do it much, much more often. But for the longer polymers we say see this much stronger spiraling. Yeah, it's maybe difficult to see but this little bullets. These are all spirals. And if you watch carefully, and I can't tell you where to look. Then sometimes you see that the polymers unspiral, they become extended they move they come on this polymer sheen and they spiral then they spiral again. There's quite the significant concentration dependence which you see here in the blood on the right. Yeah, so if you first look at the spiral numbers so that is how many times the polymer is around around itself, or you can call it a winding number if you like, this is the blue parts and averaged over all polymers. The concentration is very low, all polymers spiral there's hardly any extended chains, but as the concentration increases, polymers hit each other they help to unspiral and therefore the spiral number quickly goes down as a function of concentration. And I'm also the clustering increases that's the red bullets, and you see that as as the spirals decrease polymers become more extended they collide with each other and form clusters and that you that is indicated here by this cluster numbers. This is now at the highest packing fraction of what we had in the previous graph maybe I go back so 0.2 this is this is here so that's the, the largest, largest concentration. And now you see at low packing number on the left, we see the formation of this big mobile clusters, mobile clusters. And this is actually very similar because the persistence thing is relatively large right here's the persistence thing is 16 times larger than the length of the chain so this is essentially stiff rods. You see the stiff rods they collide they form this big clusters which collects more clusters and so on. And these are are quite stable also their motion is very persistent. Now if you do hard rods and you increase the pickling number this clustering even increases. But if you do this for the flexible chains you see something completely different happens these big clusters actually break up into smaller clusters. And this is a game, because the clusters are very flex followers are flexible and they can easily avoid the. This is this strong deformations in the in this big clusters. And so from these simulations we can then construct the face diagram, again persistence link versus pickling number. This is all for the same packing fraction which I just explained to you. And then you see, again persistence link high pickling number moderate, you see the big, this giant cluster which you saw on on the light on the left movie in the previous transparency. So if the pickling number you is high, you see it breaks up into small clusters because of the familiarity. And if the pickling number is very small you also see no glasses simply because the propulsion is too weak. Again, the, the transition between the chime clusters and the this break up into smaller clusters with increasing pickling number is again given by the same relation which I emphasized before that the persistence link is proportional to pickling number. And that is this dashed line which you see here in the face diagram. I also want to show you a few results for it, even bigger volume fraction so this is point eight so that means essentially everything is full with polymers. Again everything is in 2d which I tell you, and now we can look at again propulsion for very small pickling number. And you see not much is happening. Again, I have an issue. Yeah, so the we call this the champ face, then if the pickling number increases, then follow me start to move and align themselves. And this leads to this laminar ordering, because the flexibility is still small, relatively small compared to the propulsion forces and the most spectacular behavior is seen if you go to really strong forces. And then you see what we call a turbulent phase. And I think it looks pretty turbulent. I compare this with a movie which I showed you in the beginning of what here is marvelous. And I think that is at least some apparent similarity that it looks actually quite, quite similar but we have not looked at this into more detail yet. So we call this turbulent phase. Well, our justification for calling this turbulent is if you look at the power spectrum. Yeah, and you see the definition of the power spectrum here of K K is a wave vector. It's the equal time correlation function of the velocity. It's a different positions separated by a wave, a vector R, and then just free transform respect to this position vector. But this is a quantity which is often looked at in hydrodynamic turbulence in the classic turbulence. And there one finds that the, this is a power law behavior. This is the famous law of Kolmogorov, that this goes like wave factor to the minus five over three. And what you see here on the, on the left, our results for this flexible polymer in the active turbulent phase. And you see, they all also show the power law decay, which we take as an indication of this active turbulence. The power law is a little different but it's not 1.6 but 1.2. But of course it's also probably a different kind of turbulence. But this is still under active investigation. So if you look again here at the face diagram you see a similar behavior as you would expect, you go from jamming to laning to active turbulence with increasing peckling number, but jamming and laning becomes more dominant as the polymers become stiffer and therefore act more like straight rigid rods. So let me briefly summarize this part. So I think I've shown you that active polymers have a complex dynamics and collective behavior. That single self-propelled polymers show the spiraling at high flexion number and that for collective motion, we see that flexibility leads to glass to break up at relative low concentration and to active turbulence at high volume I didn't have time to talk today about active brownie polymers, which is a different, not a potential propulsion, but each bead in the chain has its own propulsion direction. So this is for another time. All right, so before I come to my next part, I would say, maybe we can have a few questions now. Can I start with some, so when you discuss the first single polymer, you had the spiral formation and you see that the polymer switch from the spiral to straight configuration, right? But then is it like when you calculate the rotational diffusion, are you calculating the average rotational diffusion? This was only in the polymer regime. I have not included any spirals. In the spiral regime, of course, the rotational diffusion would be, I mean, there would be no rotational diffusion at all. There would be a linear increase of the angle of the vector, which has to rotate with a constant velocity. Otherwise, if you would average over two, yeah, you average over a diffusive regime and this bubbleistic regime of the rotational motion. Sure, thank you. Yeah, Rajesh, can you unmute? Yeah, so my question is, if you turn on hydrodynamics, you don't have hydrodynamics here. So what is going to happen to this exponent and you still see this sort of turbulence or things are going to change? This is my first question. Yeah, okay. And let me answer this question. I mean, yes, turbulent, of course, changes many things, and it's difficult for me to say exactly, I mean, to say in two words, what is exactly changing? I mean, maybe we can discuss this a little bit more detail at the end. Okay, another question, has anybody looked at this in the presence of obstacles? So you have a bunch of obstacles and you have these active polymers and many, many of them. I'm not aware of one right now, but maybe one of the of my collaborators can help. We can discuss later. Thank you. Mithun? Yeah, so I had one question regarding this cluster formation that you showed. So it seemed like there was some sort of density banding. So there's the high density clusters who are existing with a low density phase. Yes, absolutely. Is that a long time stable phase? This sort of density band that appears? Yes. And secondly, inside the clusters, is there any sort of polar order that develops or is there a pneumatic order? I mean, okay, you saw, okay, the question is, I mean, when I talk about chime cluster, of course, this is always quote, quote, a two phase coexistence, because otherwise you would not see a cluster. A cluster means it's in a sea of low density. Yeah, so therefore, I mean, when I talk about cluster design, so maybe I can just go back briefly to the phase diagram. Right, so here on the left, I mean, if you go to high persistence length, so on the left, this is many small clusters. Okay. Again, of course, in a sea of essentially no clusters or in a background with just individual, then come the chime clusters. Yeah, that was in the movie you saw. And it's in this surrounded by this gas phase. So you can think of it as a consistent coexistence of the quote cluster state and the dilute state. Okay. And then of course at high, you can again have many small cluster, many, a little larger clusters in a sea of smaller clusters, so either you think of it as a phase of bigger particles moving in quote vacuum, or you think again as a two phase coexistence. But I think this is more complicated by because the glasses are not so big. So the easiest I think is to think of it in the, in the chime cluster there you can think of it like a two phase coexistence. Okay, then, and then your second question was about the polar order. Yeah, this is a polar order when you, you see this here. The, all the particles I start the movie again, the glasses move in a certain direction. And this is, I mean, the filaments are polar. The filaments are all moving in one direction, you could have in principle also an ematic state where particles moving opposite to each other. And I think you see this here in the, in this case here in the middle. It's very difficult to see up here for example here on the top. Yeah, you see the particles are moving to the left on the bottom particles are moving to the right. So it's not impossible, but I think the normal case is that it's a polar cluster. Okay, thank you, thanks. Yes, thank you. Yeah, I also have a kind of a similar question. So I was wondering whether the size of these giant cluster or the extent of the landing of this landing phase here. Also is some kind of universal so that if the system size increases then the giant clusters just get infinitely large because it seems me to me at least from the first impression it seems that there is also some self amplification for some finite size effects. Is this. So this is, yeah, this is, this is a good but very difficult question and I cannot really answer. The problem is, it depends of course a bit on the density and blah, blah, blah. But the problem is, but I mean you see this I mean if you go a little further here right I mean you see essentially you get a cluster which is spanning the whole system. And then you would say okay now it's a finite size effect right it forms a big band, but maybe it would not form this big band if the system would be bigger. But it's simply very difficult to make a simulation for a bigger and bigger and bigger system so we have not been able to answer this question but I mean I would also my feeling would be, yeah, it will not form forever one single band, but the band will start to break up into smaller pieces. Yeah, thank you. I have a question on the turbulence state that you showed. So different from 180 turbulence, your turbulence breaks down at some point in there is a characteristic length scale associated with that. Do you have an idea what that length scale is your system. No, not really. I mean this is actually a problem, which is not only in this simulation but the same appears in other kinds of active turbulence yet people have looked at it for example, at various bacteria I'm not. I'm not the one is not this practice marvelous which I was talking about but E. coli and some other shorter polymers and you see this active turbulence and there's always this peak, which as you correctly point out is not seen in hydrodynamic turbulence. And, but I think there is to my knowledge there's not really a good explanation where this peak comes from. It's typically, I mean I'm not even sure what we have here. It's basically about an order of magnitude below the peak which are the position which would correspond to size of the of the particles, and this is what happens for the bacteria I'm not I mean I've not looked at it from this point of view here. So I cannot tell you. So the question is no I don't know. And I think there's no clear no good explanation at the moment. Okay, thank you very much. Can you please. Yeah, thanks. I have a very basic question. I want to write this cluster formation is it very similar to the cluster formation in spherical self profile particles or I mean is there a simple physical understanding of. I mean, in principle, it's similar I think it's a bit different from that because I mean here we have some aligning system so if two particles come together they hit each other they align. And maybe move in the same direction but that would lead to the product the cluster or maybe move into opposite direction that would need to a pneumatic ordering. But this is different from spherical particles or disk particles right because they would bump into each other, and there's no alignment so they. Even if they hit some apparel they will not move somehow in the same direction or align their propulsion directions. Therefore it's a little different difficult and different sort of difficult different kind of clustering right in in the spherical particles, you would not see this elongated glass, which are moving forward but you would see more stationary clusters, where all the particles essentially points towards the center roughly point towards the center of the cluster. But but still the the general mechanism I think is not so different but it means particles hit each other they move in parallel for a little while. In the in the meantime, other glass other particles come from the side they hit this little nuclear nucleus and in this way the these clusters grow. Thank you very much. I would like to ask the question yourself. Yeah, I just wanted to know what is the color coding in this movie, I mean this color. The color coding is the orientation. Yeah, so that I can't tell you which color stands for what but if the particles are whatever moving upwards they are blue. And if they're moving. Let's see. But if they're moving downwards they're greenish. If they move upwards they're blueish if they move whatever to the to the left then they are regularly. Yeah, so just shows the direction of motion of the different parts of the cluster. So I don't see any more questions. Okay good yeah because we should really start to. You can go ahead with the next one. All right so maybe I tried to speed up the next part a bit. So, as I say this is now about active particles in cells or in in your membranes. And this is just a reminder from the review article by blanche in 2014 about mechanism how cells are believed to move due to acting to normalization and. And motor proteins. Yeah, so all I want to say is here there are many active filaments inside this membrane shell, and they lead to the, to the propulsion to the motion of the cell. I'm going to start with a very simple model again in 2d. This is very similar to what I've shown you before we take this little active filaments which I hear this chain of blue beads. Doesn't want you to allow for it to proceed and and these little rods in this case we have no flexibility it's a stiff rod. They are propelled in the forward come on. They are propelled in the forward direction, but they are anchored to the membrane particles, either at the front, or at the end. So in this way, if because we can have anchoring at the front of the end it can either be filming push towards the membrane if they're anchored in front, or they can pull on the membrane if they are pulled at the end. And then if you have several filaments we have a repulsive interaction but we take a finite repulsion so if that particles can actually overlap or actually move across each other. And this is given by this overlap energy are you can think of it as a capped Lenny Jones interaction. And in addition, we have a membrane friction with a membrane with a substrate. Yeah, so this ring this membrane ring which is moving on the substrate has a friction with the substrate and the particles themselves also have a friction with the substrate. So now let's see what what happens. The previous, of course, determined either whether we have pushing particles pulling particles or mixed system with both pushing and pulling and important is the peckler number, the end this repulsive energy. The repulsion is very small, you are equal KT that means the party can easily move across each other. The repulsive energy is high, then they form this little clusters. Yeah, and now you see a very different kind of motion. Yes, for this pushing rods which are then aligning because the repulsion energy is very small. And they are essentially aligning parallel to the membrane moving around the membrane, and this leads to a very erratic, random walk like motion. I have no idea what I'm doing wrong. Okay, anyway, so base if you have pushing and pulling rods, but then you see this little cluster here of pulling particles and a little cluster of pushing particles and they exert a torque on on the cell and therefore in this you get this circular motion rather persistent circular motion. If you have only pulling rods, the pulling rods also form this little clusters and this is a smaller peckler number that's why cluster formation is more pronounced. And you see this rather persistent motion in one direction which arises from all parties pulling in the same direction, most part many particles pulling in the same direction. So this was just a warm up of course it becomes more interesting if the membrane is actually deformable, right because then the party was not only push or pull move the cell but they also deform the membrane. And here we can again distinguish three different classes, this kind of fluctuating shape where the cell shape does not does not change much show some active fluctuation. The carotid side like shape just think of the picture of the carotid side which I showed you in the beginning. I'm not going back to all to the beginning. Yeah, and in this case this, all this pulling roots, also lead to a flattening of the membrane in the rear. And then we have this kind of shapes which you call notofill shapes because they resemble little, the shape of notofills. Now what is interesting is that if you look at the deformability of the shapes and the motion of all these different objects for different number of for different propulsion strength for different number of rods inside. And so on then we find there's a can be a classification of of the shape and and the velocity. So all the particles which are here for negative as far as to be these are the ones which have a extension. So the orthogonal to propulsion direction. These are the carotid side shapes, and they all have roughly the same velocity. I mean not the same velocity. I don't tell you exactly what scale means, because it becomes a technical but it just means of course if you have more rods and they push more strongly, then it's clear that the velocity increases but that has been scaled out here. So the trivial factors have been removed. So by the same. I mean this scaling is done the same for all the different shapes. Yeah, so you see that this is the carotid side glass. This is the this notofill glass this is a kind of a slightly different neutrophils all the neutrophils are here. So these are the fluctuating shapes because they have essentially zero as far as the and roughly no, no velocity. So the point I want to make is that there is a close connection between cell shape and cell motility, if you have this internal driving. It becomes interesting if we now look at the interaction with such object with hard walls or with interfaces. Yeah, so in this case we here look at the hard wall so we took a look at this shape, and it starts the hard wall is somewhere around here. On the right hand side of this figure, and it approaches the wall under various angles. And then you see in this particular case it actually starts to move along the wall. I mean this is more easy to see here in this movie. Yeah, the wall the wall is here on on the flat part on the on the right and you see the pushing filaments push the particle towards the wall therefore it does not detach from the wall and the pulling filaments they all keep pulling and therefore move it parallel to the wall. Yeah, this is different if if you look at the middle figure in this case we have only pulling filaments, and you see that part again with different. This makes me nervous. Anyway, okay so in this case you see again with different incidents angles that it's not sticking close to the wall but due to the rearrangement of the internal filaments, the particle actually the cell is actually reflected from the wall. And this is actually quite similar to what has been observed in the experiments. This is a character side moving on a surface. And here is some textures part of the surface which the character side does not want to to touch. Yeah, so it acts a little bit like a hard wall, and you see it bumps into the wall. It reorient and it moves away from the wall again. And if you look at this. This is analysis of this experimental movie you see that many different incident angles. This is a flat incident small incident angle this is a very large incident angle, but all of them come out when they're reflected come out with roughly the same incident angle, and this is very similar to what we also see here. But then there you see that we have the different incidents angles, but many of them here come out at essentially the same reflection angle. All right. Maybe I go through this very quickly so we can go do something similar for for a friction interface so that the friction with the substrate it is different in the gray region, and in the, in the white region. And let me just show you this movie because in this case again we can have this capturing by the interface. Yes, the particle come the cell comes close to the interface. You see that the green bullet here shows that there's actually a tank ready motion of the membrane, because the friction here on the, on the white side is lower than on the, on the gray side. Therefore, this leads to this rotational motion, while the cell is actually propagating fell to the interface. So let me come. And this can also be compared with experiments and let me just skip this, because I want to say these the few words about about the three dimensional case and this is also in collaboration with experiments. This is now really three dimensional vesicles and we have many particles inside the particles and now I really spherical particles. I explained this here. Maybe I should start the movie because this is quite a long movie. So this is the experiments were done up by other collaborators at the age to reach. So this is trying to limit lemon vesicles in this case it's Janus particles Janus fields which are driven by this hydrogen peroxide reaction. So this is the standard diffuser for the particle, and you see here in the case of low tension, the particles cluster from this little cluster, and they pull at that I started again. That's what they cluster, and they form this little tether here so a few particles are clustering and you see a tether is different, that is difficult to see but you see it still somehow not moving away so this must still be connected to the to the main vesicle. And this is for low membrane tension if you do high membrane tension, the membrane tension is so large that it somehow prevents this tether formation to happen. So, we have done Monte Carlo simulation molecular dynamics, whatever you want to call it simulations for such a system. In this case we take active browning spheres for the self propelled particles and the fluid vesicle is described by a dynamically large membrane I don't want to go into the details. Now, and you see a very similar behavior. You see that particles cluster they form this very strong tethers. And this is a regime now where the tethering is quite pronounced, because there are, this is a strong propulsion force therefore it's more pronounced than what you saw on the in the experiments. And here is a comparison between experimental shapes of some mentally observed shapes and what has been seen in experiments and essentially you have to look at it. In this way that the top row shows this what I've shown you in the movie it shows this formation of the tether. And here is a similar configuration which has been found in the simulations. Similarly here this is the movie I showed from the simulations, and you can so see similar tether with several particles here at the bottom of the experimental graph, you can find here for example, strong, more strong deformations of high concentrations or even the formation of this baller like shape here at the bottom. So overall I would say there's quite a good correspondence between an experiment and simulations. One advantage if the simulations is that you can easily vary the peculiar number the, the propulsion strength. This is actually quite difficult to do in these experiments, because if the concentration of hydrogen peroxide is too large, you find bubble formation of hydrogen bubbles, and that somehow makes the whole system very complicated and difficult to interpret. And therefore the experiment was essentially done just by a single propulsion strength, whereas here we can construct the whole phase diagram as a function of peculiar number here, upwards and particle volume fraction in the x direction. We can see that there is a regime of fluctuating roughly circle shapes, if the propulsion strength is high, usually the tether formation, and then if the particle concentration is very large, then we see this formation of ballerite shapes or baller type vesicle shapes. Yeah, and I can give you a little explanation, hand waving explanation for how this happens. Well, there are two competing methods or maybe three competing mechanisms. Yeah, the one is that of course self propelled particles generate a local force on the membrane. It's very similar to what people have done for colloids which are attached to the membrane and pulled by an external laser tweezer, and then they see this tether formation. Now in this case, the force is generated, not externally by laser tweezer but internally by this propulsion strength. If that propulsion strength is big enough, or this force is big enough, then it overcomes the bending rigidity and tension of the membrane and then you see the formation of the tether. So the propulsion works against membrane rigidity and tension and whatever dominates either you see the tether or not. Yeah, and of course tether, you need a big enough force and therefore this happens at large activities. So this is essentially for if you think of a single particle. Yeah, and if you think of many particles but then they come can form clusters and that leads to a stronger propulsion force and therefore this enhances the tether formation. At the moment, they also cover a larger part of the surface so particles are pulling or pushing on different parts of the surface and that is called a swim pressure. And that's why if you think of the Laplace swim pressure as a Laplace pressure that acts, generates an active membrane tension. As I've seen in this experimental movie, in this case it was a passive tension, but if the tension is too big, then this surprises the tether formation. Yeah, and we can put this into a creation I will spare you from going through this in detail. I'll show you the results. Yeah, so this little theory is the here the full and dashed line. This is for single particles and that explains the transition from these fluctuating vesicles to the formation of a few tethers. Yeah, so this becomes more difficult with increasing particle number because active pressure appears. The second line is here for clusters if you allow particles to cluster, but then this becomes again more easy to form tethers therefore this line goes down. But if the concentration becomes even bigger then again also the active tension starts to become even larger and therefore the active tension again, suppresses the formation of individual tethers and you see rather this kind of global vesicle deformations. Okay, let me just not go into the details here just want to say we can also look at the fluctuation of the particles rather than this would be really mainly here where the vesicle is still roughly in the spherical shape. We can still see the effect of activity to do to enhance fluctuations that we're not going to the details just look at the results. Yeah, so this is the fluctuation modes, the fluctuation modes. This is again a two dimensional cut to this three dimensional vesicle, therefore we have only one wave number which you can think of the wave number with mode number L. Yeah, and so what you see is for large wave numbers a short wavelength fluctuation. This is essentially the same behavior which you would expect for passive particles. But for low wave numbers. This is behave the behavior would expect for passive vesicles with some small tension. But in this regime, the activity plays a big role. This changes the power law behavior from L to the minus one extra to L to the minus four. And you see, either to exponent the bluish line here corresponds to the large L behavior that is roughly constant. But for small L, you see this dramatic change as a function of Peckley number. If the Peckley number is zero you have L to the minus. Okay, this is this is this middle regime, which is very stable essentially no. Sorry, sorry, this is L to the minus one which you see here but then as Peckley number increases, you go to higher and higher exponents or active fluctuations become more and more prominent important for small wavelengths, and you can see a similar behavior here. Also in the experiments. So let me just finish. I'm not finished anymore. Okay, so my conclusion about the second part is the cell motility is determined by this interplane of membrane deformability, external friction and boundary forces, the internal force reorganization and the pushing and pulling the existence of possible and pushing and pulling filaments. I've shown you that this is the emergence of cell shape velocity and sensing together, sensing in the sense that particles this collective this complex party we can actually sense the wall or sense an interface. So we have this, yeah, this is this next point is scattering deflection at interfaces maybe an interesting approach to study selectivity, and in the final, finally I've shown you the sculpting of as equals with external with active particles and that leads to many interesting non equilibrium shapes. Tonight, I would like to thank all the members of the theory of living matter group here in newly this was in part funded by the DFT priority program on microscreeners. And of course I would like to thank you very much you for your attention. Thanks a lot. So are there more questions from the second part. Can you can I ask you one question so in one of the early slides you had for the flexible membranes. You had this relation between you know you're the grouping of different motility with that's very city. Right in one of those you had this base diagram. You are talking about 2d stuff right. Yeah, so, okay. Yeah, yeah, so that's right. Yeah. So, is there any simple explanation for this sort of connection like grouping of this motility for as far as city or this difference is happening. Is it because the changing active forces or is it. The change of the active, I mean, the, the trivial factors have have been scaled out. Yeah, if you say I mean if I take twice as many filaments of course the propulsion strength is twice as big so the velocity is twice as big roughly speaking. So therefore we have divided by the number of propelling filaments and we have divided by the activity. So that is scale out. So, so what I think what you see here is the effect of shape that's what that means if you have essentially a spherical object, a circular object, and the pulling forces are somehow randomly distributed because not okay I should say, maybe this is a point I've, I've not emphasized enough. Yeah, so here, here in this case that all the pulling filaments are collected here in the beginning here on the front, because if there's a curvature. Then the pulling particles some are collect at the region of high concavity. Yeah, that's because they are pushing forward and if it's concave, then they have a difficulty to, to move away from it. If it's convex, then of course they can move easily very easily away from it. Yes, so therefore they are collecting here in the front and the pushing filaments, they try to flatten the membrane where they're pulling on the membrane therefore they are trying to make a curvature in the opposite direction and there they collect for the same reason. Yeah, and so therefore you have this ordering that all the pulling and pushing filaments are more or less pushing in the same direction, and therefore they are moving quote quickly. And now if you, if you look at the neutrophil shape, and I maybe I should explain, which I have not done before. So we have two neutrophil shapes the mono and the bike. And the reason is that the mono means there's one region in front where all the particles are pushing forward, and all the pulling particles in the back, and they do not do much. Because they are quote opposing each other in their direction of propulsion. And the by shape has also a little cluster of pushing filaments in the rear which is pushing in the opposite direction, but for the same reason, but it's a highly curve region and therefore they, they collect. And therefore the body is moving less quickly than than the mono, the mono shapes. Okay, I hope that explains it a bit. Yeah, so when you were showing these experiments in the Janus particles and yes, you said that changing the speed of the particles is different because of experimental constraints but for the experiments that were done. Is it possible to estimate what, like where in the Peclet axis, I should try to look at if I were trying to correlate these experimental results to the simulations. Yeah, I mean, this is actually, unfortunately, more difficult than, than, than it seems right because I mean if you, if you look at the experimental shapes, then I would say they are. If you, if you look here. But, and of course, I mean, so they can of course also change the concentration but that is of course possible right that you also see here right these, these, these, these case here is of course, can you see what you can see my pointer. Yeah, I can see the mouse. Okay, so, but here of course they have more particles inside than than here on the top. The concentration can of course be changed. Yeah, but then, and then if you look at the shapes we see here, and you compare it with a face diagram, but then, then he would say okay it must be here somewhere in the middle. Yeah, Peclet order whatever 150 200. Okay. Yeah, but, but if you do the calculation, and you say okay how fast is this particle actually moving without a membrane. And then you get a significant the smaller Peclet number, right, I can't remember the number exactly around 50. But, but, as I said, but I think it's a little bit more difficult, because, but the particles are mostly close to the membrane. So we don't know exactly what this means for say the high parasite concentration. It could be depleted locally. The hydrogen peroxide diffuses in from the outside and therefore it actually a higher hydrogen peroxide concentration. You also don't really know what happens if they move in a tether. So, again, that's that is there is there hiding hiding dynamic flow with which changes things so. So, okay, so, so long story short is, we have not been able to really make a detailed prediction of Peclet number and said okay and this is exactly this this part in the face diagram. It's more of a qualitative comparison. But regarding this other thing about, like you said you are changing the concentration in the experiments but does that match up sort of like it doesn't lead to more of these prolet shapes with increasing concentration. I mean there's another stuff, which I didn't tell you about the experiments. So I answer your question, you have to remind me about your question in the second, but the experiments are done in a in on a cover slide. Yeah, so the, the, I think they have probably a high sugar concentration or maybe the particles are heavier, and they sink to the bottom and flatten somehow. So this is not so what what you see here is somehow pancake like shapes, which you see from the top or from the bottom, but they have not, they are not have not the same extension normal to the surface. Yeah, so so therefore we compare three dimensional simulations with exactly two dimensional about it's also not really two dimensional. It's somewhere between two dimensional three dimensional in the experiments. So that again makes the comparison. More tricky. So now but please please remind you about about your question again. So you're saying that whether it is observed in the experiments that with increasing concentration you get more of these prolet, prolet shapes that was there in phase diagram, the simulation phase diagram. Yeah, I think that is that you see here right I mean, if you look again. So the, the, the, the, this, this top part is the low concentration and then here this lower left part is the higher concentration and you see, we are here for example this bullet shapes or this almost to connected by a small tether or here. I think they also saw some topology changes which we could not do because I mean our by construction our membrane has a fixed topology. I see. Okay. Thank you. Thank you. Monica. Yeah, so in the flexible polymer. So what is the idea behind. What is the idea behind the modeling of the membrane and the spring connected polymers. So do we see such something similar in the experiments. So you are talking about this kind of. Yeah, yeah. Well, I mean the idea is essentially to model the the cytoskeleton somehow, right to say, yeah the cytoskeleton is this active filaments which push against the membrane, either driven by polymerization or driven by, by motor activity. So this is what we try to, to mimic by these filaments whether this is then due to polymerization or to motor activity I think that's to see what order does not make such a big difference right because you can think of a moving polymer a moving rod also by thinking I cut a little piece away at the, at the end and I added in the front. Okay. Yeah. Anything. Yeah, thanks for the great talk. So I have a question from the first half. This is Nathan here. So in that motility essay of acting filaments I think they also saw a phase where there was traveling bands of filaments, like a layering of filaments so did you did you see that in your simulation in any parameter space. I mean, we never saw a banding. I, and I don't nobody who has looked at self propelled rods has ever seen a banding I mean there's a little exception. I think there was a simulation by having Friday and under a spouse. And they also take problem like chains actually I mean, a model is quite similar to what we are doing for the flexible polymers, but they have done it on a lattice. So I mean the, the, the polymers move on a lattice they have only discrete orientational, I mean so so each, each, each bond somehow of the chain can only have a discrete angle in in space and I think they saw, they saw the bands but this is the never understood what what's the difference between this, this model and, and our kind of model, all I can say is all the Richard Roth models at least have always ever seen these kind of clusters, similar type of justice which I've shown you here. And I mean for our polymers chairs we also have only seen the summer elongated clusters never the bands. So some subtle, subtle thing. I mean, we were discussing the continuous version of the which of a witch egg model recently. And I mean, this is kind of surprising. People have, I mean this is not our, our observation but people have seen that if you take a witch egg type model in the continuum, you have to be very careful to to say how you make this alignment rule. And depending on how you actually do it, you may either see bands or you see clusters. So my feeling now is that this is really a very special effect of this which type models that you see the bands. They're not directly putting in the alignment in direction alignment rule right like that they're they're repelling each other hardcore repulsion and okay. Yeah, we have hard core repulsion and there is a little bias. I mean if they collide there's a little bias in the forward direction which comes from that this is a chain of beats. There's a little kind of friction, which I mean when these chains of beat beats each other there's a little kind of friction, which prefers the alignment in the polar direction rather than the alignment in 180 degree direction. I see. I see. Okay, thank you. I would say from my point of view. I mean this is a very valid question a reasonable question. And it always was in the back of my mind but you said never never managed to. Never managed to really clarify it or I mean we never looked at it in much sufficient detail to really clarify it. Okay, okay. Thanks. Thanks. Are there any more questions. Okay, so if there are no more questions I would like to thank her for this wonderful and exciting talk and you know we had a lot of discussions around the results. So, yeah, thank you. And our next clocking will be in June, June, and you will have Ignacio. Thank you all for coming and for my discussion. Thank you. Thank you very much.