 Zamo se z tem saj. Druga tebe. Prvom nrolo poločenjo, svoje organizacije din moj, zato je bil vse navršen za posločenje, kom, ki sem tko nadal... Pri lasti se izgolejo, očas ili je mi brel miles, in tebe ga peničo izgole s prolastv. ... v zelojnjih roli sketchesin, k dév prvストosti roli tisti. Zelojno v到on niči vzeloj svetnja, da se vzpečila vsega načinje, in zelo vzpečila vzpečila. Prepoče sem začala, da sem se različila, in kako sem prišljala, nekaj je prišljala, ki ješlje, prišljala je svega, zelo vsega, ko je vsega, in ki je vsega, je vsega, da je počak, počak, Max B, Jim Boyang, Michael Czakowski, Mateo Paoluzzi. Vespečne včešče je tudi vključila z grubami Georgeo Schitta in Roberto Cervino v Milanoj universitičnih. Sela je tudi nekaj komplek, ali po pravih tukovosti, zelo sem zelo, da se zelo načinje, da se zelo načinje, z zvajenjem kontrakciju in kotljenje, z ko je stajnila in vzpravil je instihljevosti, ki je evočno se vzpravil s kamikalim energijem in začeli s mechanicali vzpravili. Zeločijo je je zeločne vzpe, zeločijo 10 v mikro per hour, nekakšno mladke, danes način, da je prijevak, kako je materija, nekako lepe. V njimeljih tih, njimeljih vzpravil je, način, peterinjelj tih, kajest, kajest, general, jone substrajt in levin, tisy sels move kolektivli in naoji, jih zame moving of a wood, wood deli in gas, se jaz iz kod, da, where the epithelial cells march coherent li, to fill in the wound in the tissue? And of course another great example is one that Tamač, we check already showed this morning in a different system. This movie, noop, okay. What happened? This movie down, nah, it doesn't work. Tukaj da je v vse, je... Hmm, pa moj mous. Okay. Ah, bojte, da je tukaj vse. Okay, tukaj tukaj na vse je našelj več, in je tukaj izvršenje tukaj. In pri vse, svej se dobro vse vse da se prišli vse povedi za dobro, a pri vse, se prišli za vse, in počkosti, način, kdo lahko še pripelj, bi ide se prišli, da bi je zdivati ljudje, ki so rečen, da so počkoli se. Na Slovene je vzreša, da še počkoli je uПa pa začnučen tอยosti, ki te imaš i zo bote. Neči se je počkoli, da bane počkoli je, če se tijto vse tijto vse tijne začne. Vse bane dovolil svu prej nekaj delatim, in mi je, ki bo, da bo zelo načkoli, ki so počkoli počkoli dopozibiti tijto vse tijne, and how they are determined by the properties of individual cells. Let me show you a couple of other examples before I go discussing. I'm a theorist, so I will describe you some models, but I want to show you a couple of other examples from experiments. So here is another epithelial tissue. These are actually cells from the lung from the group of Jeff Redberg at the Harvard Medical School. And what it shows is that as time goes on, since day three, day six and day ten, this tissue actually gems. Cells over here are moving as they would in a fluid, but eventually after about a week, they gem into solid light behavior, and this is highlighted at the bottom where you can see the individual velocities that are tracked by particle image velocimetry from this tissue. So cell layers can gem over time, and as you can see, this is an example of what's called the confluent tissue. That means that the cells, there are no gaps between the cells, the cells completely cover the plane, and so the density of the area of fucking fraction of the cells is not really changing in the system. Something else is driving the gemming. And in these other examples, these are actually breast cells, again a confluent layer of breast cell. To the left is essentially gemmed, you don't see a lot of motion, but then when you add a particular protein called RAB5A, which is associated with endocytosis, essentially what happens is that the tissue becomes a fluid and exhibits these large scale coherent flow-like motions. These are actually experiments from the group of George Ashita at the University of Milano. So cells can, cell layers, tissues, can tune themselves between solid light and liquid light states. Now, we are familiar with this kind of behavior in active systems, meaning systems composed of entities that are just like cells, are active and motile. And in fact we know that we can actually go from sort of an active gas of particles moving around in random direction to something like a flocking active fluid as we increase density. These are experiments back by some time ago in skin cells, and as you increase the density, you see that you go to essentially a packed system and the velocity vector show at the bottom becomes smaller and smaller, so the system is slowing down, there is gemming due to crowding. But in this confluent tissue, as I already said, packing fraction is one, cells cover the plane, so the collective migration and the changes between fluid light processes, some mechanical feedback, cell-cell interaction, and actually cell shape changes occur in the tissue, certainly not by density. And so we need a new type of model as compared to the agent-based or particle-based type models that many of us have been using to describe flocking or collective motion. So what I want to do today is essentially tell you about some models, the models that have been used quite a bit in developmental biology to describe this kind of system, but by assuming them to be in equilibrium with active matter models that is adding motility essentially to these models in developmental biology to try to quantify the materials properties of tissues. And I will show you essentially two things. First of all, I'll introduce a model that actually shows a liquid-solid transition tuned by density, by cell motility and by cellular shape. And then I will add some kind of alignment interaction and show how that can drive flocking and coherent motion of these cell monolayers. And the parting gray is actually, I just want to advertise it, we recently actually developed a continuum model of the kind of system I will show, the kind of model I will show you in a minute, which is sort of like a toner-to flocking type model, but instead of coupling to density, couples to an order parameter field that describes cellular shape. So, there is a well-known model in developmental biology known as the vertex model, which is a model mesoscopic scale model of a confluent tissue. Again, here is my tissue, if you look from the top, it looks like a foam, what you see in white are the cell boundaries. Of course the cells have a finite thickness, but we are going to make it completely two-dimensional model where your cell monolayer is in the plane, is a translation of the plane with polygons. The degrees of freedom in the original vertex model are the vertices of the polygon, but in my model there will actually be the area and perimeter of the polygon, so each polygon is a cell. And people usually write down an energy for such a tissue, which incorporates, of course, some physics. There is a term where cells tend to adjust their area to a target value, and this describes the fact that the layer itself is incompressible, but cells therefore can change the area in their two-dimensional model by adjusting the height, that's what this term is supposed to describe. There is a term here that describes proportional to the square of the perimeter, that describes bulk contractility. There is essentially a network, a polymer network, which tends to contract due to the actual motor protein, and that is tends to affect the perimeter and this term is essentially a line tension proportional to the perimeter and the line tension itself has a sign physically, the line tension, that is how big the perimeter is, will be determined by interplay between cell-cell adhesion that tends to make the perimeter bigger and contractility of the cell that tends to make the perimeter smaller. I've chosen a minus sign in a regime where actually adhesion wins. The perimeter tends to get bigger because that's the interesting regime for our purposes. I can use the square root of the area A0 for my units of length and complete the square in the perimeter and rewrite it for my energy as quadratic in both area and perimeter and when I do that, the model contains two dimensionless parameters. This is essentially the ratio of the coupling constants Kp and Ka and I will really not vary that very much but the key parameter is the ratio of the perimeter the target perimeter to the square root of the target area and the target perimeter of course will depend on the line tension. So this that I will call target cell shape is the measure of how anisotropic the cell is for a circle this will be a number of about I think almost 3 for a pentagon if a regular pentagon is 3.81 for an hexagon is 3.72 the more anisotropic or elongated the shape gets the larger this number is. So that's the model that has been used in biology to actually relate the cell configurations to the forces that are present on the edges of the network in equilibrium and what people generally do is that they minimize this energy with respect to the position of the vertices and the cellular rearrangements the main type of cellular rearrangements that occurs in these tissues are known as T1 transitions these are kind of rearrangements that can turn your tissue into a fluid because they allow for neighbor exchanges you go from a situation where the two white cells are neighbors to a situation where the two cells are neighbors and to do that you have to overcome an energy barrier when my colleague Lisa Manny did a few years ago she actually studied the statistics of these energy barriers and she was able to show by minimizing energy that the mean energy barrier if you plot it as a function of this target shape parameter actually vanishes above a value about 3.81 which is close to the value for pentagons suggesting that above this value the system is a liquid because this transition can occur with no energy cost and below this value is sort of a solid so what we did then was to combine this model combine this vertex model energy with active particle dynamics construct a model that we call self-propelled Voronoi model that describes now a confluent tissue where the tissue is now we actually use really a Voronoi tessellation of the plane and we assign also to each cell a motility which is in the direction which is of fixed magnitude and is subject to orientation and noise so the dynamics of the Voronoi cells of the centroid of the Voronoi cells is controlled by self-propulsion with direction randomized by rotation and noise and forces which are obtained from this tissue energy I showed you before and the really interesting important thing is that these forces are multicellular you cannot write them as pairwise additive and they are not just among nearest neighbors so this is a more complex type of interaction the particle type interaction usually used in the agent based model so if you simulate this model and calculate say the mean square displacement of these cells or polygons as a function of time for increasing value of the shape parameter p0 what you find is that for large p0 the system is a fluid mean square displacement is linear in long time and for small value of p0 it becomes solid like the mean square displacement doesn't grow in fact more precisely you can define a diffusivity as an order parameter and it will go to zero at the value of p0 that now depends is close to 3.81 and it depends on the motility of the cell the cell propulsion speed as well as the time scale for the rotational noise that determines how persistent the dynamics is and in fact you can construct a phase diagram this axis is the cell motility v0 this axis is the target shape index and you find the transition using this diffusion coefficient as your let's call it order parameter between the solid and the fluid the solid have a small p0 so they are effectively rather round and regular and they don't stray away they are caged these are the path of the cells and in the fluid they are more elongated although it's hard to see by eye and they move around the system like a fluid this parameter p0 really is the interplay as determined by the tension which remember is determined in turn by the interplay between cell, cell adhesion and cortical tension so surprisingly the fluid occurs in the regime of large adhesion that's because tells like to create more adhesion by extending actually their boundaries and well that's just to image the fluid and solid like behavior we just call it the few cells just to make a sort of a nice movie here the really interesting thing is that you can actually define actual order parameter for the transition that is if you actually measure the mean shape of the cell so that is take the ratio of the perimeter of each cell to the square root of an area of each cell what you find is that in the solid so this is different from the target shape parameter which is the parameter of the model in the solid this is locked to the value 3.81 because essentially in a regime where area and perimeter are incompatible and in the liquid it just grows linearly so you have a continuous phase transition from the point of view of the structural order parameter between solid and liquid behavior and the reason this is interesting is because it means that prediction here that can actually be validated in experiments is that you can actually determine whether the tissue is a fluid or a solid by measuring the mean cell shape and in fact if you take this q and set it equal to 3.81 you produce a line in the phase diagram that pretty much coincides with the place where the effective diffusion constant goes to zero and in fact a couple of groups have tested this prediction by measuring cell shape these are again the experiments by Fredberg at Harvard and although well this biology so there are big error bars but as you can see as time goes on and the tissue jams the mean cell shape seems to approach this value of 3.81 in the system and similar results has been obtained in breast cell by the group of George Oshita so that's so what I've shown you here is that we have a model for a tissue that includes motility and cellular shape rearrangements and cellular shape changes and produce an active solid liquid transition tuned by motility and cell shape it doesn't quite yet get to this idea of how do cells coordinate their motion but clearly it's important to know the nature of the material to know how cells or whether cells can actually move through it next I'm gonna tell you about sort of adding alignment to the model to produce actually a system that can also actually move in a correlated way that is flock and in other words I want to ask the question how now to cell actually correlate their motion as seen here in this protrusion which is a finger like protrusion again in a wound healing assay so well one simple way to do it is to simply add an alignment interaction to our model that is modify the angle of dynamics here not just now rotational noise but in addition we have an alignment of strand J each cell tends to align its direction of motility or polarization with the direction essentially of the mean force which is internally essentially the same as the velocity of the cell and so now we have a new parameter in addition to our cell shape parameter sorry I called it P0 before S0 and P0 are the same thing we have the alignment strength and then we are gonna keep the motility and the persistence of the dynamics we are gonna keep those fixed what you find is that if you now try to make a and this is just a pictorial phase diagram I'll show you a quantitative phase diagram in a minute this is in the plane of the strand J of alignment interaction and that shape anisotropy parameter so for low alignment interaction we have the same two states we had before a solid state and the group of cells has only been colored to show you whether the system is a liquid or a solid so in the solid they stay together in the liquid they kind of fall apart but the mean velocity in these two states remains zero for higher alignment interaction of course the system flux it has a zero mean velocity in the solid this blob of cell just moves along without much deformation in the liquid it gets deformed so quite fall apart as strongly as they do in the absence of alignment and in fact if you look at the system a little bit more closely what is now plotted here are the cellular paths in the rest frame that is in the frame that is moving along at the mean velocity the red bar denotes the mean direction of motion and as you see this flocking liquid seems to have quite a bit of order most of the displacement in this rest frame are transverse to the direction of mean motion and in fact if you actually measure the structural property of this what we call flocking liquid it turns out there are actually is a smectic type state there are rows of cells which are kind of squashed in the direction of mean motion and fluctuating a little bit in the transverse direction and the per correlation function shows more strong correlation along the direction of motion which is the red then in the direction perpendicular to motion which is the blue so more quantitatively so we have bought now a solid liquid transition and we have also a flocking transition how do we quantify those well for the solid liquid transition we use again the mean square displacement and this effective diffusivity that I introduced before for the flocking state we sort of use conventional order parameter which is essentially the mean direction of motion and then you can also calculate the fluctuations in the mean direction of motion sort of the susceptibility which will have a peak at the location of the transition so here is the flocking transition between non flocking and flocking solid these are the this is the order parameter that goes towards 1 for increasing number of cells increasing system size and here is the susceptibility that gets more and more picked as you increase the system size and here the same thing for the liquid state with a very similar behavior so the sharpening of the peak of the susceptibility with system size suggests that these may be a continuous phase transition unlike in particle models with nearest neighbor interactions and in fact if you plot the location of the maximum of the susceptibility as a function of system size you see scaling and in other words this system is much more similar to particle let's call them particle models with so-called topological interactions which is not surprising because the energy itself and the forces that drive the dynamics are indeed topological in nature in this system and I think for the people in the audience that work on Vichyakti models and would be interesting to kind of look a little bit more closely at analogies between and correspondences between this model and possibly the triangulation network that you can generate in the particle models with topological interactions so here is now the phase diagram a little bit more quantitatively again alignment interaction and shape index P0 so we have a static solid and a static liquid for low alignment we have a flocking solid which is a state that has a finamine velocity and zero diffusivity and the flocking liquid which is a state with finamine velocity and finite diffusivity the red and green points are obtained numerically the blue line is actually an analytical estimate which is essentially obtained by making a model of a cell as a caged flocking particle calculating the mean square displacement and equating the effective temperature you can get to that to the typical energy barrier that will be required to escape from the cage and as you can see it works actually quite well with only one adjustable parameter here which was actually the same as was determined for the transition for zero alignment and the black points if this works ok the black points are sort of a semi analytical estimate again that is estimated for the transition between flocking and non flocking liquid essentially for the liquid to become flock that is to move in a correlated way it has to be that the rate of alignment is faster than the rate of structural rearrangements you always have structural rearrangements in the liquid but when the rate of alignment is faster than those then you can get this flocking liquid and you can actually compare perhaps not quite quantitatively but there is actually a nice comparison with experiments that can be done by calculating a four point density correlation function which is familiar in glassy physics in the sky four which essentially look at this curve in red this is in the liquid it will have a peak the location of the peak of this four point correlation function sort of describes so what you have in this dense liquid near the transition you have the sort of packs of cells are moving together and the location of the peak in the sky four essentially describes the lifetime of the peak describes the size of this coherently moving pack of cells and as you can see in our model the green is without alignment that would be the non flocking system and then you get this great announcement here when you have alignment you have these correlated motions that are seen in the experiments but actually experimentalists have also calculated chi four from their data and you see a similar behavior with the peak and notice that as time goes on in the liquid the peak moves to shorter time meaning the system is becoming more and more liquid and notice also that there is a big difference so just like in our simulation between the size even though these data look the same the scale here is 10 and this here is 150 so the peak in the flocking liquid where you have these correlated rearrangements is much larger than that where rearrangements are very localized so let's see if I have a few more minutes I think I do so I told you I started out showing this one dealing assay and saying that one of our goal was to understand our cell correlated behavior to move together and clearly this alignment interaction is one possible mechanism but so far we really only looked at it in a system with periodic boundary conditions and actually no boundary moving coherently and there is actually another type of calculations and modeling you can do for this system to answer the question so we gonna go back to wound healing where the key question that has been actually around for some time is how do cell transmitting information to correlate their motion and move coherently and fill in the wound so let me see if I can get these to go again so this is the front of cells epithelial cell in a wound healing assay from the level of Javier Trepine, Barcelona and what is shown here in color are the forces that the cell exerts on the substrate as they are moving along and that red is forces to the left right Lewis forces to the right but the main message from this picture is that all cells are exerting forces of about equal magnitude on the substrate and a long standing question in this field has been whether, so what drives the motion and for a long time people thought that the motion is driven by so called the leader cells that essentially pull the one behind but clearly this is not so here because essentially all the cells are participating in this force generation that gets transmitted throughout the entire layer and by the way time scale for this kind of dynamics again is ours cell move really slowly this kind of epithelial cells so the key experimental finding that is associated with this idea that all the cell are participating in the dynamics is that and again we have here again an expanding cell layer and again what's in color is again the force that the cells are exerting actually you could think of this color as a measure of the local pressure in the system and the experimental finding is that in an expanding cell layer like this information is actually transmitted via propagating mechanical waves that is if you sit right say at the middle of your expanding monolayer and the measure for instance the variations in cell area which correspond to variation in local strain of the system so they describe local deformations you actually get this periodic behavior you get traveling like waves or ripples in cell density much like sound waves in air of course these are very slow traveling waves they travel millimeters per day but they are traveling waves you can see them by measuring cell area by measuring local strain or actually by measuring stresses which can be inferred from a measurement of the forces of the cell exert on the substrate and it turns out you can actually capture this behavior even more simply than with the kind of mesoscopic model of Voronoi models that I just show you with a very simple model by describing your cell layer as an active elastic continuum and what do I mean an elastic cell sheet with elasticity cost for elastic deformation but the activity comes from forces that are internally generated through the coupling through these motor proteins that transform chemical energy into mechanical work and if you incorporate the dynamics of these and the dynamical turnover of these motor proteins that gets bound and unbound from the network that constitutes the cell cytoskeleton these you get a dynamical feedback between forces and protein activation that actually results in traveling waves and in fact here are the traveling waves in again the strain rate in red the stress in solid blue and the strain in dash blue obtained from this simple continuum model which I thought I would mention because I thought I would have interest in people here and here are so called chemographs that these are plots in color of the local deformation for the monolayer time is down distance is in the middle so you start with a monolayer which is only this big and it expands and the blue and red denote positive and negative deformation and these characteristic cross structure indicates that these are in the traveling waves as seen in the experiments these are actually deformation rates both of them of the deformation measured in experiments so and actually one of the things we are doing now is to go back and look in more detail at this one dealing assay using this mesoscopy of anoint model to more precisely try to understand the interplay between sort of pulling forces at the boundaries and these turn over chemical forces induced by the motor protein so I think I should probably try to conclude so what we've been trying to do are essentially our big goal here is to construct a phase diagram for tissue and actually this is not a cartoon this is quantitative and the phase diagram for the model I showed you contains is the axis what I showed you before is just the slice in the motility cell-cell adhesion plane the cell-cell adhesion is controlled by this parameter p0 the target cell shape but we've also looked at the effect of the persistence of the dynamics that can actually fluidify the system because it enhances sort of correlated rearrangements that tend to make the system more fluid meaning cells can escape from their local cages if their dynamics is highly persistent as it often is for cells and the idea is to construct effective theories of tissues where many molecular scales or genetic parameters may be fed into a single effective parameters such as the persistence the motility of this target cell shape and these parameters perhaps can be accessible through experiments of course many things we are exploring many things that are still missing here such as the role of cell division and death the role of heterogeneities differences in cell properties the role of the coupling to the environment which is actually very important in tissue I also showed you that if you actually add to this model alignment of cell polarization with the local forces or the resulting velocity on the cell you actually get this large-scale streaming you can get these flocking, solid and liquid states and although I don't know that there is some suggestion that the unjamming driven by this particular protein RAB5A does indeed correspond to the fluid state obtained there has very strong similarities with what we call here a flocking liquid state that was the state where you saw these large-scale collective rearrangements now one interesting thing here is that we find that the flocking transition about in the solid and the liquid is continuous which is consistent with what is seen in particle models and suggests that indeed this fact the transition being continuous might be generic for all these sort of topological type models and we find these sort of structural asthmatic order and dynamic aligners entropy as well which would be interesting to look for in experiments and I did not talk about this but I wanted to mention again that we have actually developed also a continuum model of shaped driven flocking and rigid transition sort of combining these two at a continuum level and what is interesting about this model is that it provides cells have to undergo, they move in order to create specific patterns especially morphogenesis and this is generally understood by coupling to fairly complex reaction diffusion processes and the diffusion of various chemical called indeed morphogens that have been very elusive people have not really seen in the experiments and so what our work is going in the direction of suggesting sort of a mechanism purely mechanical mechanism of rigidity sensing associated with the fluid like or solid like nature of the system that could be actually complementary to chemical sensing and I can tell you more about that in another time so let me just finish by showing again the pictures of the people who did the work and thanking various agencies that provide money for those of you, thank you for listening