 Now, this mic is on, yeah. So the talk on the schedule was named host-pathogen interactions. And I do have a talk very specifically on that about malaria parasites. But I gave that in previous hands-on schools. And today, I wanted to try this other subject on you. It also, in some ways, leads to host-pathogen interactions. Because what you're seeing here is the surface of a parametrium single cell animal. It's a little animal, a few tens of microns long that swims in ponds. But a very similar situation with 10 micron active beating filaments exists in our airways. And these things are constantly beating, moving the mucus up through the airways and into our digestive tract. And keeping that surface of the airways always clean and renewed. And that is actually the first barrier we have against pathogens, airborne pathogens, like bacteria that somebody else might be emitting through cough, for example. And also, that surface of the airways is therefore also full of immune cells and the systems that the body has in place to start triggering reactions against pathogens. But today, I chose this other talk for two reasons. One is that I think it lashes on nicely with other talks we've heard through the weeks on nonlinear systems. And many of you work on chaos and synchronization and similar questions. And there are elements of that in my talk. And the other reason is more history of my own group. I wanted to show you what started off as a very, very simple project before I had a group when I was just working me with some summer students. And then the success story of how that thread became a big tree, a big funded project funded by a European ERC grant with now a team of six or seven people working on all the leaves of this tree. So when I look back to it, I don't think it's particularly my own ability that got me there. I think there were signs of what can make a good project that perhaps can be a lesson to everyone, even if you don't care specifically about the content of my talk. All right, so now I think that right. So this is actually my group today. We recognize here Nicola, who is here at the Hanson School and me there. This is Yuri, who has been a long time postdoc in my group and has built a lot of the equipment. And everybody else here are PhD students and postdocs doing a variety of things. So about a third of these people work on the questions that I will go through during my talk this morning. OK, so I compiled a rather large amount of information into 45 minutes. I apologize, I will go quickly. But the point is I don't want you to focus on all the details and all the figures precisely that I'm telling you. I'm really trying to tell you a story of how we built up bits of fundamental physics, how we started talking to biologists and medical people, and how we tried bringing all of this together. So I will briefly tell you about Lorentz number flows because that's the underlying fluid dynamics behind many of the questions that we're posing here. The core of the talk is a bunch of model experiments that we managed to publish trying to dissect the essential physics of how those beating filaments that you saw in the wave phase lock together and are actually able to generate spontaneously that collective dynamics that shows up as a wave, which is very important for the mucus clearance and for transport of fluids and for swimming. And then briefly at the end, I will show you examples of the things that we're carrying out now with biological samples and living cells that have a cilia. OK, so the Reynolds number was introduced yesterday already in Dan Goldsman's talk. It's the ratio of the inertial forces to the viscous forces. And typically, if you're thinking of an object translating through a liquid, you've got the density, the velocity, the typical size of the object and the viscosity of the fluid down here. And if this number is much less than 1, then it means the viscous forces are dominating and there is no turbulence. And the equations of motion that are the Navier-Stokes equation here. Actually, simplify a lot because you can start dropping the terms which are kind of quadratic in the velocity. And they become linear equations. So what's important is that if you are a normal sized person, even swimming slower than Michael Phelps, you will still be swimming a very high Reynolds number if you try swimming in the sea. But just plugging in the corresponding numbers into this ratio here. But if you are a small object, say a few microns big and you're swimming, say, 100 microns per second, then when you plug those numbers into here, you get to 10 to the minus 4, say, order of magnitude. So micron sized objects, essentially, because they're very small, they give you very low Reynolds numbers. And that's true also of the cilia beating. You put 10 microns. You put the typical speed at which they're beating through the fluid. And you come up with a non-turbulant flow around those cilia. And it will be equivalent as ourselves trying to swim in a jam or a nutella. So you have to come up with strategies in that situation that don't rely on inertia. You can't do a breaststroke motion that then lets you glide for a little bit before doing another one because the friction forces stop you immediately. You've got to come up with something that looks more like crawling, I guess. OK, so if we have the general Navier stokes, but then we start simplifying for a small Reynolds number, then we come up with this linear equation that I mentioned. And a lot of this was calculated already 100 years ago, or previously, in terms of what velocity profiles you would expect around bodies with specific geometries. And also, for example, if you have one sphere moving through a fluid and a second sphere somewhere else, what forces does the second sphere feel because of the motion of the first sphere? These things are calculated by stokes, by Eauzine, who are fluid dynamicists in the 19th century. Many of you know, actually, the drag coefficient if you are moving a sphere through a fluid. Certainly, in my hands-on session, everybody who went through that got reminded of this. Also important, if you're thinking of filaments moving fluids is the formula that corresponds to what happens to a cylinder, a cylinder perpendicular to its axis has a high drag coefficient higher than along the axis. More or less, there's a factor of two difference if the cylinders are of a sensible aspect ratio. And this is important because if one of the strategies for moving is to have a high drag coefficient for one part of your motion and then a low drag coefficient to recover your original conformation and then high drag again, low drag. And this way, you can make a periodic cycle that has different drag coefficients in the two parts of the cycle and allows you to actually put force into the fluid. If you were simply moving the same filament back and forth without changing drag, you would just be pushing and pulling, pushing and pulling with the same force and you wouldn't be moving anywhere. So what really allows you to have a different drag coefficient, in essence, is the fact that on a filament, each little piece, you can think of it as a little cylinder and you can move it parallel or perpendicular to the overall motion. You can position it with different angles. Okay, so another bit of physics, fluid dynamics that is underlying what I'm going to tell you later is the interaction between spheres. So you'll probably have in mind that if I'm at low Reynolds number and I move an object with some velocity, the force that I need is proportional to that velocity and the coefficient is the drag coefficients. So there's a more general systems of equation that you can write if you have more than one object. So now this kind of generalizes the idea that velocity is proportional to the force. It's now the velocity of object n is proportional to the forces acting not just on object n, which would have been the single object pushed, but the forces acting on all the m objects, all the objects in the system. And it's still a linear relation because the equations are still low Reynolds number linear stokes equations, but I have like a mega tensor here relating all of these velocities to all of these forces. And Ozean was the person to calculate what you have to put here to relate the velocities to the forces. So in general, if these guys are 3D velocity vectors and these forces are 3D velocity vectors, and I have n objects in the system, this beast here is n by n matrix, but the elements are three by three little matrices. So it can be like a gigantic thing to write out. But if I consider the much more simple situation where I had just have two objects, and I only want to think about the motion on the axis that connects them, then all of this stops being vectorial. I simply have a scalar, one scalar equation for object one and an equation for object two, but both are just scalar equations. And in particular, say if I have two spheres and I try to move sphere one with velocity one, then I need a force one and this is just the stokes drug that I think is well known to many of you. And then I also need to consider with what force the sphere two is being held and the distance between sphere one and two. This accounts for the fact that there's a fluid flow and the forces on sphere two are giving me also an effect on sphere one. If sphere two is there, but nobody's holding it, basically I can move sphere one as if that one wasn't there because sphere two will be just moved off by the fluid flow that I generate by moving sphere one. All of this is true for, it's mathematically true for point-like objects. So it's a far-field theory that's was made to get to here. All right, and this is the more general form with kind of bold vectors and matrices. And what I've written here is actually the more general equation with a noise term. So what I'm thinking now is if I have microscopic objects, I want to write the Langevin equation. So I want to write the equation of motion with my external forces, these forces of interaction that depend on the velocities of all the beads and the ozine tensor and also a stochastic force that moves them about. Well, there are some details about what you're allowed to put in this noise term because since the particles are coupled through the fluid flow, the noise term also needs to take, it needs to know about this coupling. Otherwise you're violating fluctuation dissipation theorem. But that's just a detail. If you're thinking of doing simulations of moving spheres, then you've got to kind of put a sensible noise term in the system. But the most important thing that I want to stress is that these hydrodynamic forces decay as one over the distance. And that's in physics, we always think of it as a very long range interaction because one over D takes a long time to go away. It's not an exponential and it's not a power law with a high exponent. And it really means that when you have a system of lots and they're moving, you have to think of it as a many body system. It's like, it's one, you can't really kind of cut off this interaction and expect to be calculating the right properties for the system. Interestingly though, if your spheres are doing what they have to do close to a wall, say imagine they are now close to this pavement and everything is full of liquid, then the boundary condition given by the pavement changes this interaction and you get a power load that decays as the cube of the distance. So for objects creating their fluid flows next to a wall, the interactions are much more short range and this difference is going to turn out to be very important to describe waves. It's much more difficult to come up with a situation where phase oscillators will assemble into traveling waves. If you have the one over D interaction and it's much more simple if you have the one over D cube because it looks much more like a nearest neighbor interaction and if you've been to big stadiums where people stand up and do the traveling wave of standing up because they're very happy and it's a way to pass time as well, well that is a nearest neighbor interaction which creates a traveling wave and that parametrium, the cilia and that parametrium are doing an analog of that kind of Mexican wave around the stadium. Okay, so this work really started about 10 years ago. We had just built optical tweezers and we were able to trap colloidal particles and one of the things we did was we trapped particles in this case, you can see three, these are 3.5 micron diameter particles, then we trapped four, five, et cetera and in this experiment, the traps were fixed, they didn't move. So it's actually a very simple, if once you have optical tweezers, it's kind of almost a simplest experiment you can do, you just have a static trap. And we just had several static traps and managed to put a colloid in each one. And what we did in this work was we studied the fluctuations of these kind of particles put in this polygonal arrangements and it turns out that the, if you look at the cross correlated motions in these thermal fluctuations, then they are well described by the Ozine tensor. So this was really just a check that we had learned properly how to think about the Ozine tensor in this situation. And the reason why we could actually publish it as a paper was also that these polygons are so regular that the Ozine tensor matrix has a very simple form and you can write it down analytically as a simple formula, even for the case of many, many beads and you can diagonalize it analytically. So for this case, we could calculate the eigenmodes and eigenvectors of the Ozine tensor which meant we could characterize the correlations in these fluctuations. And that's kind of, no, with traps on, they are jiggling and you let them jiggle for several minutes and you record all these random jigglings. Yeah, no, they're important. The traps are creating harmonic wells. So each of the particles is in its own well. And then in addition to being, you could do the same experiment just with one and that's what everybody does with tweezers to calculate how strong the trapping potential is. But now there are several and each one is in its well. And then as well as the harmonic trapping, that they've got the interaction through the velocities. So our tweezers had a device called acousto-optical deflector which is basically a bragg grating that you can, where you can tune the spacing by putting a radio frequency field. It's a standard kind of opto-electronic gadget that you would have to buy and then control. And this way a single beam can be time shared between different positions on the focal plane because you can, much more quickly than any dynamics in the system, you can steer the beam. Ah, yeah, so we were careful. Yes, it does because it's the same one beam which gets shared between more and more positions. But in these experiments, we were careful to calibrate so that we had the situation where we were weakest with, I think our maximum was 10 beads that we could actually trap. And then the other experiments we did reducing the laser power. Thanks. Okay, so I will skip the maths. And the other thing we were doing very early on as well as static traps was try to think if we could move beads to create fluid flow. And this links to what Dan was telling you yesterday. This very nice kind of Purcell idea of scallop theorem. Maybe I can get the scallops to swim. Don't know if everybody has seen scallops. So the scallop only has one degree of freedom. It can only open and close with one angle. So Purcell said, well, such a thing, a low Reynolds number cannot flow, cannot swim because you are doing a motion which is reciprocal in time and the equations are linear and you will just end up putting the same amount of force into the fluid in one direction as in the other direction if you just do that. But of course these scallops can swim as the YouTube video shows. And that's because they're not working at low Reynolds number. They're making a jet. So they're playing with inertia. And then Purcell went on to show to make this simple set of, well, three linkers. So two angles and all of you are going through the robotics lab where you play with a version of this. Not in water, but as a robot on land or in beads. And anyway, so Purcell suggested this was in some ways the simplest object capable of swimming, of self propelling. And that was, in what year was Purcell? It was early 20th century, I think. So then much more recently, Najafi and Golestanian who were at the time working in Iran and then Rami Golestanian came to the UK. In 2004, they published two or three theory papers where they calculated the hydrodynamics of a situation with three spheres whereby changing the distances between the two spheres they could play the same game as the angle in the Purcell swimmer. Actually Professor Desimone here also has papers on the efficiency of when you have more than one of these sets of three sphere swimmers. But the idea when you have a single three sphere thing is you change the distance, say here I change the distance on the right, I move the right bead closer up, then I move the left bead closer up, then I move the right bead out, and finally I move the left bead out. And this sequence is different, meaning it's symmetric left to right if you break time up, down. So it knows about direction if you give it a knowledge of time and it will go the other way if you turn time the other way around. So this object is non reciprocal in time and as Purcell had said and Rami Golestanian and Alina Jaffee had calculated it should be able to swim. So we didn't build it as a robot, nobody has done that on the micro scale yet. What we did was just position these things in the traps. So there are no physical linkers, but with the traps we could move these distances and we could study whether this object worked as a micro pump. So we were holding it so it's not swimming around but by doing these moves again and again, if it's a swimmer it should also be a pumper. And indeed it pumped, we then calculated that if it wasn't a pump but it was actually a swimmer it would go very slow, but not zero. Okay, this is in real time how we did our experiments and then we played with various parameters of how much we moved and how fast we actuated these moves. But up to now, so this is now not a static trap but we had learned how to precisely code the timing so that we could do these moves and then we just repeated the moves. Up to now there hasn't been any clever feedback. So we just recorded the movie and then studied where are the traps, where are the beads and work out if this, from the movie you can work out if this is pumping or not pumping by being very careful about where are the lasers and where are the beads and what are the net forces at every instant in time. So you measure the trajectories, you also compare them to simulations which are the solid lines and you integrate out to calculate whether this is actually putting a force into the fluid. So it is putting a force of hundreds of piconewtons as a result of this non-reciprocal motion. Okay, so the swimming, the equivalent, well the pumping flow which would be equivalent to swimming velocity would be of 0.2 microns per second which is, it's poorer than say an E. coli swimming much slower. So this was published and lots of people started looking at this paper in the community because it was the first simple experiment after a series of theoretical papers that have proposed similar things. Okay, so what I'm gonna tell you now was the second phase. We had learned how to build a tweezer, how to do that first initial phase of simple experiments and then we wanted to do experiments on synchronization to go from how does, in some sense we had looked at how does a single object manage to create a little bit of a pumping action. But then the more interesting question to us seemed, okay, now that you have in the natural system we have hundreds or thousands of these individual little pumps and clearly they are synchronizing and phase locking, how can we do kind of some basic experiments to understand why they're phase locking? So there is no brain, there's no electrical impulse coordinating these things, this is a single cell, probably there's not even like a calcium signal. So these are what we think, these are actually talking to each other through the fluid flow. So we wanted to do experiments that only had fluid flow, by again moving colloids and work out what consequences and what kind of richness of properties we could get just by playing with the type of motion and the rules of motion that we could give to the individual phase oscillators. So there are some simpler biological systems that people look at and they stand as kind of intermediate models between what I will show you which is just moving colloids and the real important questions which are these big waves that we, well waves on a large scale that we have in the airways and also in the brain, the fluids in our brain are also moved about by these and we would die immediately if our cilia stopped busy. So this is an algae called claminomonas. In these two movies it is held by a glass pipette and this algae only has two cilia. So it's a very beautiful system to do microscopy on and most of the time it swims with this motion that looks like a breaststroke swimming and it goes straight. Again, those of you who've been through the hands on with Nicole and myself have seen this in our microscope and then sometimes it doesn't synchronize the two cilia, it has them out of phase and in that situation, the algae chooses another probably random direction before switching back to going in phase and going straight again for some seconds. And so this you might think is perhaps a loss of synchronization. Maybe the system is positioned such that a fluctuation has some probability of displacing it from in phase synchronization and giving it some time in a not phase locked state. That's the kind of idea that we can explore with colloids. So I will skip that movie. So what did we do? Well, the principle is that we're now thinking of replacing each of the beating cilia with just one of our colloidal particles and we then want to jiggle it back and forth. So in the natural systems, these things beat somewhere between 10 hertz and 50 hertz depends on the system, but they are conserved. I mean the one I showed you on the algae has the same molecules as the one which is present in the human being. So they are one of the most conserved organelles from plants to animals and they go a long way back in evolutionary time. That means they're very efficient and very complex and you can't really evolve it again in a slightly different way and not easily. So okay, so in what sense can we change that very complicated object to just assume that it's a beat? Well, we are keeping a few things. We can keep a similar frequency and we can keep similar fluid dynamics because if these things are not too close to each other, then the fluid flow that they exert on each other is actually fairly well described by the fluid flow that we can generate with a sphere. So the fluid dynamics I think is not so controversial. What's more controversial is this thing, as it beats, I told you it has high drag, low drag, it is flexible, it can fluctuate, it's very rich, it has a lot of degrees of freedom. And actually I will show you a picture later that what's going on inside is itself a very rich dynamical system. Molecular motors are grabbing on, putting a little bit of force, falling off, there's hundreds of these molecular motors constantly attaching force off and all of that is force responsive. So inside here, there's a lot of feedback. Okay, so we are coarse-graining all of that complexity into simply moving one of our spheres, but we do have some room to keep track of those degrees of freedom. We can, for example, we can move fast and slow, we can change our profiles, we can move very rigidly or we can allow jiggling during our moves and those are the kind of simple physics points to start to try to account for some of the complexity going on in the cilium. If the cilium is very flexible, well we can do the jiggling but with soft traps which still allow fluctuations in during the periodic motion. And that's the way we've headed into this problem. We've been trying to make kind of experiments that at the same time had a well-defined physics and we could back them with a bit of analytical argument and numerical simulations, but also always having in mind what the biological system was so that we could actually talk to biologists and tell them that we were trying to answer the questions that they thought were important. All right, so if you want to study synchronization, you can't just move beads the way we did with the micro pump because there the kind of the phase relation between the beads was fixed by us. So it don't go to study synchronization by fixing the phase locking. You have to allow the phase to be free. So we came up with two strategies. One is dragging a bead on a closed loop with a predefined force. So we predefined both the orbit, which is this black line, and we predefined what force we're going to apply at each point in this orbit. So in the simplest case, this could be a circle and we could be pushing the bead in the circle with a constant force. And then the phase is basically the angle that the bead is doing relative to some reference position. And if you have one, then it will start spinning at some period. If you have two of these, they will both spin. If you make them identical, they will have the same period. And then in addition to the force that we're putting with a tweezer, they also have this hydrodynamic force. So that can couple them and they might go in phase, for example. And then you can have two or say up to 10. Typically, 10 is the maximum that we can do experiments on. And in that orbit model, you can play, you can then start playing with the forming the orbits. You can play with making the force bigger at some point on that ellipse, et cetera. So you have, and you can make that orbit more rigid, like a railway, like a little electric train model, or you can make it a weak trapping. So you are weakly pushing it along and it's still able also to do tangential fluctuations. All of these things matter. And I'm not gonna show you today results of these, but you can make kind of very interesting regime diagrams of what collected dynamic comes out as a function of the details of how you drive stuff. And you can go back to your biological systems and look at the force versus time curves and try to map them onto these more simple force versus time models. And that can teach you whether, well, it can really answer the question whether hydrodynamics is the most important coupling mechanism in the biological system, which is still in general an open question. What I am gonna show you a little bit in five minutes is are the results of this other idea, another way to make a phase oscillator. I think I have a bigger, yes, okay. So we have our harmonic trap, this yellow one, and initially imagine the bead is this red bead here and it's away from the minimum. So it will feel a force that drags it towards the minimum of the harmonic well. But we image, so we don't move the yellow trap, but we image the position of the red bead very quickly. And when it comes close to the minimum, say at this dashed yellow line here, we switch off the yellow trap and on this other trap, which is a small distance away, say a few microns away. And suddenly the bead finds itself well away from the minimum of the blue trap. The bead is kind of up here in the blue potential. And now it feels a force to the right and so it starts going right. Again, we image it several times and when we spot that has reached this dashed blue line, we switch the blue trap off and then switch the yellow trap on again. And this we do automatically. It's a feedback loop. We, I should also say, you need feedback here as well to maintain constant force on the bead. You need to know at every instance where is the bead and you need to put the optical trap a certain distance ahead of the bead to give it a constant force. Here, also there is feedback. You need to know where the bead is in order to decide if you're going to change the trap position or not. And when you let this go, then your bead is going back and forth with a well-defined amplitude. But the period is a kind of doubt and also most importantly, the phase is completely free. So if there's another force from somewhere else that pushes it along a little bit or the phase will advance or if you have several of these things, they may or may not synchronize with each other. And here, the most simple kind of things we can play with are the shape of the potential. So I've drawn here this curve which is a sub-bad parabola. But you can also have say a V or you could have potentials that are curves the other way around. And again, the idea is we've got kind of a playground of physics that physicists will care about and perhaps synchronization experts. But we can also go and talk to the biologists because we can try to mimic with the shape that we're putting here. We can try to mimic what say the claminomonas algae is doing as a function of its beating. We can put something that has the same curvature as a function of where you are on the phase as the real biological system and see what type of synchronization comes out. Okay, this is a little animation of what each phase oscillator will be doing and we can have from one to 10 of these guys. Okay, so our first experiments were with two and we did games such as moving them more far apart. So this Q is basically an order parameter. It tells us how much synchronization there is and whether it's out of phase or in phase and zero is no synchronization. Well, the color code is how much, these are the distributions of Q over an experiment. So the color tells you how peaked a certain phase lock is. So in this case, these were harmonic chops doing this active motion that I call geometric switch. By moving them close, the distribution closed up and became peaked and in close to anti-phase phase locking and moving them away, you lose synchronization because thermal noise starts kind of shifting you off the phase lock. This is just the same curve. So this Q close to one means anti-phase motion and as you move them away or actually this plot is as you de-phase them. So you can also do typical games that you do with phase oscillators, they might have identical frequencies or you can get them slightly off and you can study how to what extent this phase locking is robust as you de-phase them and then if you go to multiples of the frequency you might find another region of phase lock and these things happen also with these hydrodynamically coupled oscillators. As I mentioned, we can basically with the optical trap, we were becoming, so this is now like four years later, we're becoming better at playing with the optical trap and by time sharing, by time sharing very quickly over neighboring positions, you can create optical landscapes. So instead of having simply harmonic traps, you can play with putting very quickly different harmonic traps all over the place and the sum of that will look like a potential that you can decide, you can have potentials that even have kind of almost like harmonic upside down if you want to. And this, these movies should give you, should show you how important it is to, how important it is to, this may, okay, good. How important the potential is. These are the harmonic ones and they go in anti-phase, which are the curves I've shown you up to now. If you put sub-harmonic, they actually go, these two beads synchronize in phase and if you put lines, the beads don't know how to synchronize. This is because a line has no time reversal and so there's no information there about whether you should go towards synchronization or away from synchronization, the result is you don't synchronize. What, that, this is anti-phase, this is in phase is actually a long story. I don't have enough time to explain to you, but we got to the bottom of that. And this is kind of, as a function of the curvature of the potential, you actually get this nice kind of transition from phase to anti-phase and we use these experiments in relation to this clambidomonas organism that has been measured very accurately by lots of groups. And so the positions and the speeds of the phylogenome have been published. You can go back and calculate what the force is and compare it to the simple things that I've shown you up to now. Okay, as well as the potential, also how you lay out your oscillators is very important. Some of you are playing with networks, so I thought I should show this. So three is a frustrated system because I've set them up so that they all want to go in anti-phase and I'm jiggling them along the tangent, but the three can't go out of phase with a, can't go in anti-phase with everybody else and actually it turns out that most of the time it decides to go all in phase, which would be the most counterintuitive thing. The even polygons can fit the out of anti-phase between neighbors and that's what they do. And the odd ones, so five and seven, et cetera, they set up a traveling wave clockwise and anti-clockwise at the same time. That's not obvious by eye, but if you analyze those motions you, that's what you get. Okay, so that also we made sense through the Ozine tensor. And in my last few minutes I just want to show you where the project is going now. I mean, we're still doing some colored experiments because the biological systems, a lot of them are doing what they do in viscoelastic liquids. And so we're kind of pushing that frontier also with the simple systems. So learning how fluid is pumped and how synchronization can happen if you have both viscosity and elasticity in your liquids. But also a lot of effort is going to these cells which are human airway cells. So these are movies from the lab. This beating is happening at around 10 hertz. So the movies are a little bit slowed down. Those, these are healthy cells and let me just, right. You can see very, very flexible filaments. Asymmetry in what they do in one direction compared to the other direction. These are all signs of a healthy, well-structured decilia that are doing what they should do. Let me show you a bad one and then I go back to that. Oh, give me a bad one. All right, so there are various genetic diseases either of the cilia or of the mucus that give you bad beating. So this is, this is a genetic disease. It's fairly rare, but those people who are born with this have a lot of problems. And this is cystic fibrosis which is much more common and it's a disease of the mucus. So here the beating is impaired because the mucus is too thick. So those are the reasons why there's actually a community of doctors as well as biologists who care about these cilia. So I told you that they are conserved. The molecular structure is essentially the same from algae throughout all of the animals. They are 100 nanometers wide these filaments and tens of microns long. And they have these microtubules in blue. These are fairly rigid structures that are present also in other parts of the cytoskeleton of cells. And then there are these molecular motors that cause a sliding, put a force between the microtubules and allow the tubes to slide against each other and the overall cilium to bend. And this I mentioned is itself a very rich non-linear system because it spontaneously sets itself up to beat at 10 hertz. And that is itself, I mean there are a few groups looking at that but nobody has a nice clean model that can be used as an element together with them coupling more than one together for example. So you really realize how there are, this is a question that spans scales and areas of expertise. And it's actually a very broad, it's a big, big question putting everything together. Okay, so we're putting our cells in that these are airway cells and they like to be in contact with air. So they receive, there's a little dish so that they receive liquid from below and they are exposed to air from above. And one of our questions in fact what Nicole is trying to answer is whether we can determine if these collective waves that these cells have are they sustained through the hydrodynamic coupling which is what we had in the models of colloids for sure or is there something else, is there perhaps vibrations which they can propagate to each other because they are in contact. And to do that, the first experiment is to try to put like a little dam and see if there's synchronization left and right and then also try to kind of dig a trench and see if there's synchronization left and right. So these two experiments together should be able to tell us if the wave is being sustained by hydrodynamics or by contact. And maybe Nicole in a few months will be able to tell us the answer. We don't yet know. And the other thing we're doing is these movies. Okay, we basically that cell culture can be bent and we can look at the profile and that's how you can get those videos of the cell themselves beating. And in those movies, okay, let me skip ahead and then I just need to come back for a second. In these movies from the side, you can actually trace. It's going slow. You can do segmentation this at the moment we're doing by hand because it's quite tricky. You can segment the position of one particular cell as a function of time. And then this is color coded by what is the curvature along the filament and what you see as a function of time and going up the psyllium, so the arc length from zero is that there are traveling waves of this curvature. So the shapes of the psyllium are actually, say, it's a kink which is being pushed from the base to the top. This is, in airways, this hadn't been measured before in airway cells. In sperm cells, this was known that the sperm manages to swim because it's making a sinusoidal wave that it travels to the back. I was surprised to see that actually something evidently very similar is happening also in these other cilia here. Okay, so in the very, very last minutes, and then I will stop, I just want to connect to what you're doing in our hands-on. So we developed, so when we have the cell culture dish situation and we make a movie from the top, then this is what the movie looks like. So here at the scale of the cells, so the black things are basically cells. So this is a movie at fairly low magnification, but it's what we need to go and look for collective waves. And in fact, if you stare at this for long enough, you can convince yourselves that there is, there are patterns of synchronized motion on a scale which is bigger than the scale of a single cell. It's almost like also a little vortex here, but there's definitely things are beating together on a scale of say between there and there. And to quantify that is not so simple. In the past, people had simply tried to look at the Fourier transform locally, and then that gives you kind of quite complicated and noisy data sets. And that's where we went to this DDM technique that some of you have seen in our hands-on that relies on taking image differences, well, a video, then image differences, Fourier transforms of that, and looking at the essentially the dynamics of the Fourier modes that come from these image differences. It's a very powerful technique, and in this particular case of the complicated movie, it allows us without any need to segment anything and without setting any image analysis parameters to get both the beating frequency of the psyllium and perhaps more interestingly, by looking at how these signals decay as a function of the lag time to get an idea about spatial and temporal coherence of the psyllium beat. Okay, so for those of you who are interested, perhaps you should come and talk to me. The way we get spatial coherence is to compare this DDM analysis on a whole set of boxes of different size. And as you go to a smaller and smaller box, you're analyzing dynamics, which is on a smaller and smaller scale, and you get more and more coherence motion. And this transition here is as a function of what area are we choosing as our area to average on essentially, and we get a transition in the decay time at a scale, which corresponds to a few cell diameters. And that means that in this cell culture, where the cilia were not particularly aligned, it was just how they've grown, the synchronization distances is a few cells. In our real organisms, through development, the cilia actually grow very well aligned and you would expect then the metaconal waves to be able to propagate over distances even beyond a few cell diameters. So I apologize if I crammed a lot of material in. Oh, this is where it goes very slow. I've shown you, I've given you a flavor for the basic physics. In my mind, I also had the idea that I've shown you what we were able to do 10 years ago, which was very simple, and what we've been able to build up, which has been both through being better with our experiments and by learning better what were the actual biological questions and the medical relevance of what we might be able to approach. And what we're doing now is actually working with these kind of real cells and getting ready to receive cells from the hospital as well from patients that are being cared for by clinicians. And that should be kind of an exciting new phase for our future. Thanks.