So I have to. So good morning everyone. Thank you very much for coming. It's really nice to see such a turnout of people here. We've got good weather and we've carefully organised it. So it's eights weekend. So if anybody wants to go down to the river this afternoon, it's a great place to watch the boats, to eat ice cream, to drink Pimm's and to play chicken with the bikes as the students try and go up and down this crowded towpath and keep up with the boats.
But of course, before we can play like this, before, like the students, we have to have to do some work. And the work we're doing this morning is it's thinking about biological physics. People have been doing really super biological physics and McLarens and doing experimental work for a very long time here and in particular, they've tended to concentrate on imaging very small things inside cells.
Biological physics in in the first century is a bit newer, and I think it comes from, at least in my case, um, it's coming from an interest in statistical physics. Um, from statistical physics. I started working on something called active matter and not just me. Many people around the world now are working on active matter, and then we sort of realise that active matter really is pretty much the same thing as biology. And we might have something to say about biological physics.
So what I'm going to do is I'm going to start by trying to explain to you what active matter is. And then I'm going to talk about a particular question in mechanical biology. How does cells move. Now if you think about it without thinking too hard, you know they don't look like they move at all. Bits of us are not wandering over. You know, we're not a science fiction movie, so bits of us are not taking off and wandering somewhere.
But in fact, we'll see this morning that cells do move, sometimes slowly, sometimes a bit faster. And our first talk about how single cells move not I'll talk about how a layer of cells, a sort of experimental model system of a layer of cells on the surface, move and then talk about whether and how this might be relevant to what's going on to real problems in vivo. I'm very much by about halfway through this talk.
We're at a level where we're doing very research when we don't understand what's going on. So if I give the same talk in five years or so, things might be very different. And it's still very much the jury's out how much physicists can sensibly say about biology in this approach using statistical physics. So we all remember. Don't worry about equilibrium statistical physics.
The gas in this room is going to come to equilibrium, and it's going to more or less sit there, more or less constant density described by the Maxwell-Boltzmann distribution with very small fluctuations. But sometimes, if the interactions between particles are a bit different, they can get. Things can happen in a much more interesting way. This is a very simple model system.
The particles are moving with some sort of velocity, and they have a small interaction so that they tend to align with each other. And then a bit of noise random fluctuations. So they tend to um, align with each other as well. And you can get very complex structures just from this simple model. I'm sure it reminds you of this. It's one of the nice things about this particular bit of the talk is you can show people in nice movies.
Uh, so these, uh, uh, birds possibly over war, possibly not over or. Um, nobody really knows why starlings form patterns like this. It's quite hard to do physics for starlings because they can. Well, it's really hard to image them in three dimensions up in the air. But also they you have to worry about free will, you know, are they actually looking at each other and trying to line up. Uh, but you can get nice patterns in things where things should start to be simpler.
For example, this is a suspension of bacteria of E.coli. So lots of E.coli sitting in a layer on a surface. And again, you're getting patterns. You're getting complicated patterns. This looks like turbulence. Things are not meant to be turbulent at these sorts of length scales. Turbulence is usually things like waterfalls. The atmosphere. Large length scales here. These things are tiny, and yet we're still getting a turbulent like state.
We're getting sort of patterns, and these ones are actually called active turbulence. To distinguish it from this high Reynolds number, these large length scales of turbulence. So these are examples of active matter. Active matter exists on all length scales. Yes. And pictures of some examples. For example nature proteins tiny proteins that move things around in cells. Bacteria and, uh, eukaryotic cells, the squishy cells that move around.
All the way up to things like the starlings and things like us. And also these things here which are called active colloids. And what's special about these systems? What makes them active? Is it that taking energy from the surroundings and then using it to do things usually move around that taking energy? Each one of them is taking energy from the surroundings and using it to do work.
It's a bit different from driven systems. For example, if, um, you push a fluid, it all moves in the same direction. These things are acting individually. They're taking in energy individually. Let's look at these particular ones. This is a nice example of what's called active colloids. And I've got a movie showing you an experiment on active colloids. Colloids are tiny particles, micron size particles. And these things have a bit of something called haematite stuck to them.
Blue thing and that slide and that puts in a suspension a solution with hydrogen peroxide in. And the point is that if you shine light on these things, the hydrogen peroxide and the haematite reacts with each other and it turns into a tiny rocket. So these things move in a certain direction. So let's have a look. See what happens when you turn on the light. And what you can see is that they start hitting each other and forming a pattern. They start forming rafts of the active particles.
And then in a minute, the lights will be turned off again. And the patterns, um, go away. And these things act pretty much like molecules doing random Brownian motion moving around at random. They will all spread out. As you turn the light off and it's because you're drunk, you're putting energy into the system. You can end up with these non-equilibrium patterns. This is a very clever experiment. It's hard to make these things so tiny, but what it does is, is nothing like the starlings.
It's still a very simple set up. The ordering you get is still rather simple. But if you look at these other examples of active matter, you see that one's a bit special. That's us trying to do it ourselves, fabricating something. These other ones are nature doing it. These are natural biological systems. And that's really what biology is, right? Cells and things like that too. Taking energy from the surroundings. We are eating food and using it to do work.
So people have realised it actually is quite hard to make active matter systems. But never mind, we've got this playground out their playground out there, which is biology, and that's great because we can test our theories on biological systems. And even better, maybe we can say something about the biological systems from this point of view of active matter. We weren't. We? The community wasn't the first to think about this.
Long time ago, Schrodinger wrote a book which is called um, What is Life? And in this book he said, living matter evades the decay to equilibrium. And you think about it, that's actually quite a nice way of thinking in a physical way. What it's like, what it means to be alive. Okay. Because if you're out of equilibrium, you have energy, you can do things. And if you come to equilibrium, it's pretty sad and it's just a bad thing. So. What we're really doing is non-equilibrium statistical physics.
How do you. Do the physics of systems which are meant to be out of equilibrium, which exist in a non-equilibrium state. Not systems which are driven like pushing water or something falling under gravity, but systems which themselves are taking energy from their surroundings and using it to do work. So let's concentrate on cells and in particular the sort of squishy cells, um, and ask how do they move?
So. Certainly I came from a background where biology was a something you didn't do if you could do physics. And b nobody knew much about it in those days. I mean, to me, when I learned about cells, it looked like this. Okay, there was a nucleus in the middle and some sort of cytoplasm around the outside, and it moved. But we never really thought about asking how or why. Or I think it sort of stuck out feelers and grabbed onto the surface, which actually more or less does.
Um, yeah, but we've got better with that. I mean, thanks to many, many, uh, people who worked on what is now amazing imaging, we have some sort of idea about how individual cells move. Okay. So this is a typical sort of cell in the body. You do have a nucleus which is blue here. You have cytoplasm around the nucleus, which in a sort of gloopy way can change shape. And the way it changes shape is due to these green things which are acting filaments. So they're basically long, thin molecules.
And these molecules due to clever chemistry can treadmill. What happens is that little bits of actin are added to the front of the molecule and then taken away from the back of the molecule. So these things move forward and push the cytoplasm in the direction that this thing decides it wants to go, often to follow a chemical signal. And then somehow it has to move forward by. Although it's pushing forward, it has to move itself forward.
It does this by putting down focal adhesions to the surface. So complicated biological molecules will hang on to the surface and then pull it forwards. That was all it would do. It would just get very long and thin. And so you need some way of its pulling in its tail. And it does that in a passive way by having surface tension like a drop, and also in an active way, by having molecular motors, motor proteins, which walk around on the filaments here and tend to contract them.
So it's like a network being contracted by these motors and pulling the tail. So it's going pull, pull, pull. Now, a physics model of this is actually very easy and actually works rather well. Physics models says right. I've got a polar force pulling this along. That's the fight. Pulling on, pulling, pulling on this surface. And it's going to be fluctuating because this thing doesn't just move in a straight line.
So a fluctuating polar force and then something to pull in the back surface tension or balanced forces which tend to pull it back to circular. And. Under those sorts of driving. These cells will do a persistent random walk. And indeed, that's pretty much what they do on a large length scale. That's the physics version. Now let's look at reality. In the body. These things move through the extracellular matrix.
What the extracellular matrix is, is that in between the various organs of the body, in many places in the body. We end up with, um, we have. A basically a gloopy network of, uh. Fibres, mucus fibres. So basically the body doesn't really have state bases in anything that's not a living cell is filled up with this extracellular matrix. These are electron micrographs of the extracellular matrix. And so if cells move they have to move through this extracellular matrix.
And I always find the next movie a bit worrying because the reality and the simple physics models are really a little bit different from each other. This is a white blood cell. And the people who made this movie were referenced at the end. We're really quite keen on the fact that they'd actually managed to image a white blood cell moving through the extracellular matrix. You can imagine that's a really very difficult thing to do. These are inside the body.
For a long time, people have have images of a white blood cell moving along a surface. You'll see some of those in the movie. Um, and the idea of this movie is that we can do much better with that, but also the way it moves, the way it moves around its cytoplasm, the way it pushes. This is the 2D version. Yeah. The way it moves around the cytoplasm is really rather complicated. And we always have to remember that the physics models are simple.
They can tell us some things. But there are lots of things that they can't tell us. So this is it moving through the cytoplasm. This is a real movie of a real cell. So white blood cell and white blood cells are pretty nippy because they have to chase bacteria and eat them. This is what we always used to show. There it is, chasing a bacteria which is going to eat. Okay. And here. It is moving around.
Yeah, that's a reference. I think that the big questions about single cell motion are now not really physics. They're the biology and the detailed chemistry going on inside this cell, which makes things happen. In my view, the exciting thing at the moment. But it's in terms of some models that you get and also in terms of matching to reality. Places where physics is likely to make the best difference is what happens if you have lots of cells.
So this is a picture of an epithelium. Epithelium are all over in the body. They're basically one dimensional sheets of cells. The skin is a beautiful example sorry two dimensional. The skin is a beautiful example of that. Most of the organs of the body aligned by these cells. And the picture here is the picture from wiki. All right. And they tend to form these two dimensional layers.
And that's great, right? Because theoretical physicists like to dimensions, everything is much easier in two dimensions. So these things are good. And one of the famous model systems for looking at how these cells move is to take the cells out of the body, where it's hard to see them, and to put them on some sort of substrate like a petri dish. So what you end up with is cells sitting in a confluent layer on a petri dish. So these things are hanging on to each other through junctions.
They're all sort of that bit like a foam if you like. And they're attached to each other through things called adherence junctions, which are junctions made by the biology. So I'm looking down here on this cell layer. I'm looking at the top of the cells. And we tend to forget if we're not careful about the fact that there's actually a two plus a bit dimensional shape here.
So it's pretty obvious that these cells can't quite move in the same way as a single cell, because if they all take off in random directions, there's going to be all [INAUDIBLE] let loose, right? They're going to be pulling on each other. That's that's really a bad thing to do. You're just going to be wasting energy. So how do they move? Well. One way is flocking. This is very like the starlings. This is a picture of cells flocking.
By flocking, I mean they all decide to move in the same direction. You see this? Um, these are actually taken actually from a, uh, a real life biological system. The egg chamber of Drosophila. The egg of a fruit fly. This is the fruit fly egg. And what happens is that these cells flock. They move round and round the inside of this egg. No one's sure why. It may just be because they're active.
And so if they're active, they're taking in energy from their surroundings and they've got to dissipate it somehow. They've got to do something. So the best thing they can do is go round and round. But maybe not. All right. And this is another movie showing the same thing. This is now in a minute we'll see the cells nicely in colour so you can follow them going round and round this chamber in Drosophila.
So that's one thing these guys do. They flock. They also do this active turbulence type thing. Remember, we have this turbulent like behaviour where things move in a very chaotic way. So this is a picture of active turbulence in cells. And I might say it sells. Plated. It sells is two dimensional. Love sells taken out of the body and put on the surface. Okay. And then they jam. What's happening is that they are dividing and so they're getting denser so it's harder for them to move.
So these guys at late times in the movie are jams. They're still wiggling a bit, but they can't move relative to each other. And. Let me tell you about my favourite experiments. These are experiments carried out in Milan, um, some years ago. And what they show is cells changing from doing this, flocking the other way around, from doing that to turbulence behaviour to doing flocking. So on the left we sort of have a picture. This is a velocity plot.
The different colours are different, um, directions of motion of these things. Okay. So here I have active turbulence with small random velocities. On this side you can see the arrows are much bigger. These are much bigger velocities and they're more or less they're much more coherent and much more moving in the same direction. I'll show you a movie in a minute of that happening. This is. Okay, so. So what makes them change from one to the other?
And the answer is that they add this chemical Rab five A. No one's quite sure what it does, but people think it locks up the junctions between the cells in some way. It changes the forces actually acting between these cells. And if you watch this five A and you look at the velocity, this is without the RGB five A. The red line is what happens when you add this red five a and you can see the velocity. The mean velocity goes up. A lot.
And this is a biological experiment. So a lot means this is amazing, right? Normally biological experiments, if you have error bars and they don't overlap you're doing really well. So this you can actually um believe. And so the next one shows the movie of this velocity thing happening. So on the left it's doing this act of turbulence, small random velocities on the right. It's what happens when you add the Rab five a large correlated velocities.
Uh. Can you move? Yes. Somehow I just play that one again. Good luck. Yes. Really makes a difference. This chemical makes a difference. We're not quite sure how, but we think it might be something to do with what's happening. Um, on the boundaries between the cells. One more way. They move. We've got jamming, we've got active turbulence and we've got flocking. The last one is what happens when I put these cells in confinement.
If I put them in a small sort of container, and this is really an excuse to show you the nice movies. All right. So this is what happens to cells when you put them in a container. Active turbulence. But then the active turbulence changes and you end up with them going round and round. It's a bit like that echo chamber in Drosophila stuff. It's probably related to that okay. So it's because the turbulence is basically cut off by the boundaries.
It becomes a coherent flow. You can see that in all sorts of different active matter. This rather nice movie is. Filament driven by motor proteins. And again they go round and round. Right. There's no external driving. They're driving themselves. They form this lovely swirling pattern. And occasionally there's an instability, occasionally in the swelling screws up and then it starts again, and then you get this instability happening again.
You can see it in macroscopic active matter as well. Yeah. Okay, so there are lots of different ways these cells move. We'd like to model it because we'd like to understand what's going on. I mean, we don't understand what's going on, but, um. But it's a start. And let me just stress, okay, that if there are any pilot biologists in the audience and apologise now, we tend to think that this.
And and in a way, trying to talk to biologists is one of the most exciting things to try and put together our approaches, which minimise any complications, and biologists who get really upset when you start trying to not put in absolutely everything. Um, and yeah, reality is in the middle and some problems are amenable to physics. We hope some will need the biological detail. Biology is very annoying. I mean, it is messy. Um, and you keep going.
I mean, if you're a physicist, you tend to turn out and think, okay, that sort of nice principle, then it's going to work and it doesn't. Yeah. But anyway, we want to model these cells. We would like a model of how these cells move. Because even though, you know it's a physics model it's only the basics. But at least then we can take our model and say actually in biology, this this happens. Can we make it do that? What ingredients of the model are most important?
So I'm going to tell you about a thing called the vertex model. The vertex model is the go to model of collective cell motion. And a call out to Yan, who is somewhere in the audience. Okay, who's a postdoc here? And it's Yan who has taught me everything I know about the vertex model and provided many of these movies and is here to answer any nasty questions you might have asked. So the vertex model has to look like these cells. So it's a model of um polygons with edges which are joined together.
So it's just a load of polygons with edges. It grew out of foam models. It looks a bit like a phone. And it's not allowed to have gaps because this thing is confluent. We need some sort of energy which goes with this vertex model. So the energy is that we have an area term which says we have a preferred area. And there's an elastic force which adds energy if I move away from the preferred area. And then we have a perimeter term which is the same, but for the perimeter of each of these cells.
So pretty simple, really. If it's going to have anything to do with how these cells move, it has to do jamming, flocking, active turbulence and what happens in confinement. So we're going to go through those one by one. Does it work? Can you get jamming. Can you get the rest of them. Yeah. So jamming. And it's really because you can see jamming in this model that people realise that maybe it is a good model of cells. Sorry. This. Oh. I was going to say it was a very busy slide.
The city can't cope with itself. Yeah. Um. Is working on here now. OOP. Phew. Right. Let's hope it stays like that. Obvious that it also thought this slide might be a bit much, but in mine. Um, okay. So sometime. So the control parameter, the important parameter in this model turns out to be the important dimensionless parameter. Turns out to be the target perimeter area divided by the square root of the target. Um, the target area. That's this axis here. Over here for lots more values.
Well, values up to 3.81. This thing is a solid. What I mean by a solid is that you need a finite force to get these cells to move relative to each other. At 3.81. It becomes a liquid, a fluid, and if it's fluid, you only need a very tiny force, an infinitesimal force, to get these things to move. Think of the atoms in a liquid. If you push them very, very. If you push them gently, they will move relative to each other in the solid.
You have to push quite hard to get the atoms to move relative to each other. Here's the centre of the cells, how they move in the solid state. They just wriggle around the fixed point, and in the liquid state, they move relative to each other. If you then increase the pushing force, of course it becomes easier to see that fluid phase. It becomes easier to get them to move relative to each other.
And what caused a great deal of excitement about five years ago is that people measured this solid to fluid transition in real cells, and they found it happened to the value of this parameter equal to 3.81. And this was very exciting. And so people then messages and lots of other different sorts of cells. And found it was between. It wasn't 3.81 but it was 3.81 ish.
Okay. And the physics makes sense. The physics makes sense that these things can be very tightly bound and look very much like a solid layer, really, of hexagons, or they can move relative to each other. So then we have to see them flock. That's fairly easy. This is a sort of be check model thing again. If you put on some sort of velocity on these particles and you allow the velocity to align. Make them behave a little bit like single cells with velocities which are correlated.
Locking works very beautifully in these models. And then you run out of turbulence. But that's a bit more tricky. And indeed, it's what we have been working on, uh, in the last year or so. And. Let me just explain as a sort of background to how you get this active turbulence, this idea of contact, inhibition of locomotion. This really shows how biology works. And, um. In a way, it's not a scientific fact. It's become a belief in the community. Contact.
Inhibition of motion was first. Um. First appeared in a very beautiful and famous paper by Abercrombie in 1953. And he indeed spent some of his career in Oxford and what he discovered in experiments. If two cells come towards each other, what they tend to do is they don't like each other and they tend to go away from each other. So cells tend to move away from each other. They tend to repel each other. That has evolved over time.
Um, so that now when people say contact inhibition of locomotion, what they actually mean is that cells behave in a rather different way in a colony when they're all connected to each other than they do in reality. And one story is that in a colony they tend not to form these lamellar podia. They tend not to want to move in any particular direction. And so they tend not to pull on the substrate and move themselves around. Does make sense that that that happens, right?
Because it would be a waste of energy to try and move in lots of different directions. But. The cells do move. So what are the forces interacting if they're not these polar forces pulling on the surface? And the answer is probably forces between cells. Forces because the cells are joined to each other and they're all wriggling about. So they're tending to pull on each other. And that slightly vague explanation is because we don't really understand what's going on.
But probably forces between cells are important. Makes sense. They are. Why do they bother hanging on to each other if they're not important? And that's become known as contact inhibition of locomotion. But there really is no firm evidence out there that this is anything but a bit of a relief, really. So what we did is we took these vertex models and we put in the interactions between cells.
And if you put in the interactions between cells. Very nicely, you get something where the velocities are rather random. And if you make those interactions stronger, you get something where the velocities look even more efficiently random. And you can look at the various properties of this state. And indeed it looks like active turbulence. And you might worry about the shape of the cells. And we do. But then we said, okay, let's take these cells and let's put them in a confined state.
We didn't put them in a box because it's harder to do a box. So we put them in a channel. And we know from active metal theories, uh, which are not to do with cells, that things will move down a channel. If you can find this active turbulence. It will move down the channel. And this is very much man's work, very recent stuff. Okay. So you put it in a channel and you wait for it to move down the channel, and the wretched thing won't go anywhere. So what actually turns out to get it right is that.
In the moguls at the moment. We dissipate the energy with friction sitting on the substrate, and they give the friction to the surface. The question was often in biology, what you can have is these cells essentially suspended in space with without the petri dish below them. And if we replace this friction type viscosity with its friction type dissipation with viscosity type dissipation. Then. Everything works beautifully and they take off and move down this channel.
So what we have now is a model which can reproduce all those four different sorts of motion in cells. Details are still to be worked out. Not just us, but many people all over the world are working on models a bit like this, and trying to compare them to experiments and trying to understand what's right and what's wrong. Um, and. Indeed, Adrian. Uh, in the last talk today will talk about.
I think while I didn't was going to talk about said that they be careful, but they have some beautiful data on how skin cells move. And we want to try and match this sort of modelling to the skin cells to find out what's right about it and what's wrong about it. And it's a fun model. Yeah. And it's a fun experimental system of just having cells on the surface. But real cells don't move on Petri dishes. They move in people. So what? When I'm talking about cell motion in people in vivo.
What sort of problems can we address with this sort of physics? And this really is I think people are realising this actually. We can say something about how cells move. Building on years of really beautiful work with biologists who are asking questions in a slightly different way. So I'm going to finish by just really showing you some movies of the sort of things that are happening in real systems.
One place is wound healing. These are, um, cells where you had a layer of cells and you basically take them out from the middle. So it's just like a human wound. And you ask how these cells then move to fill up the space. So these are real experiments. These cells are moving. They're moving to fill up the space in the middle of the wound. This is cell sorting. I love this experiment. Okay, so what this is, is as a starfish embryo, a baby starfish.
And what the experimentalists did was, um, a starfish. Embryos is is composed of two different sorts of cells, which in theoretical physics language are red and green. And what the experimentalists did is take these embryos and basically mash them up. So you ended up with the red and green cells completely random. And then they just waited. And over the next day or so. What's happened is that these cells. Started forming, uh, coherent structures.
So these things are a few green cells across. These are a few red cells across. So you get something which looks like phase separation and say an all the water system. And then it becomes even more complicated because the Reds and the Greens organise themselves so that you get all the green cells in the middle and all the red cells almost around the outside. Somehow nature is able to organise itself from a state like that. To a state like this and we don't understand how.
There are theories, but there are best partial theories. This is an example of embryogenesis in the starfish. This is the fruit fly. This is a baby Drosophila. And each of those white dots is a cell. And this is the development of Drosophila over a period of some hours. And what you see. Is amazing mechanics. The cells suddenly take off and move from one place to another. These are active particles. This is collective motion of active particles.
It shows that nature is much better than we are of understanding these out of equilibrium systems and exploiting them to give patterns. This is a very similar setup, happens very early in the life of a human embryo, where an egg which is um, originally spherical, is a ball of cells which is spherical has to change into something which isn't spherical anymore, and it does it by suddenly. In vaccinating suddenly their large scale flows.
What's happening is an amazing mix of genetics, which I haven't talked about at all. The smallest scale genetics is driving chemistry, which is somehow signalling to the molecules that they have to start these flows off, and then physics about how it flows, and we've been concentrating on the physics bit, makes absolutely clear this is a multi-scale thing of which we've looked at just one bit. So let me put it again because I think it's very beautiful. Okay.
And understanding this in the fruit fly. At the moment we are trying to do the trick which which actually we can do quite nicely with these vertex. Well, we can do bits of it quite nicely with the vertex models. And then in humans is probably the next big frontier in, in this bit of biophysics. So that's a good place to stop. Uh, citrus Sofala go into a fruit fly. And then. I'll put up my. Conclusions. Thank you very much for listening.