So for example, 820. All right. So, um. Yeah. My name is Alex. Uh, I have just joined very recently the, um, uh, the theory, uh, physics here in Oxford. And I'm really enjoying this a lot. And I want to tell you a little bit about, um, uh, the research, uh, that I have been doing that I am doing, um, and also introduce this, uh, this, this presentation a little bit with some, some general thoughts, um, on, on what is going on in the field and making some arguments.
Why? Um, I also think that physics, um, has maybe some interesting things to say about, um, processes, uh, like this. So what you see here is, you know, probably really one of the, of the atomistic unit of, of developing an organism. What you have to do, it's a single round cell that we begin with.
We are looking at this, a cross section, um, and of course, biologically what is happening in the cell division is that the genome that you see also slightly in some different contrast here in the middle through this process, it's distributed to the two daughter cells. Uh, that's uh, that, this, this uh, movie ends up with. And so this is clearly the biological one of the many biological functions of this process.
Um, but I hope you can also agree with me that it is also a very fascinating physical process, if we think about this as a materialist, seems to be a material that is able autonomously to change its shape in a very coordinated way, and our experience with changing the shape of a material. What, maybe something like this, right. If we if we take a rubber ball and we I asked you to change its shape, what you naturally would probably do is to, to squeeze it.
Um, and that's what do the job. Um, but what that means is you have to apply a force. Um, and obviously, uh, there's no one, uh, squeezing the cell that you just saw in this movie. So somehow this cell is able intrinsically to generate these kind of forces that are necessary. And clearly what must happen is that somehow all the molecules that are interacting in the system, um, must be able to produce these, these forces that are doing this.
And when I talk about interacting molecules very, very quickly in the realm of, of chemistry, and indeed, um, as we had also heard before, now in several forms, um, there are processes that convert through chemical reactions, some fuel, um, into forces, um, and uh, expel um, some, some of chemical waste. And I will specify this, um, a bit more. Moving on.
Um, uh, so through this talk and so what is it that, um, uh, we have to, uh, you know, think about when think about the physics of these biological system. Um, Yulia, um, had already mentioned some very important, uh, thinking that that Schrodinger has done now.
Um, precisely, um, 80, 80 years ago, um, laying out this basic, uh, um, idea that obviously what makes living systems different from, uh, from, from that system is the fact, physically speaking, they're kept away from thermodynamic equilibrium. Um, and I want to just add here a little bit more and connect this maybe also with your undergraduate thermodynamics, um, uh, memories.
Um, if we want to, uh, you know, keep a system out of equilibrium, one way we were taught this can be done is to what it's called a heat engine. And at the core of every heat engine is a temperature gradient. So we have a something hot. We have something called we connect this to the system that we want to study. And because we have this ongoing hot and cold, uh, we can sort of to work um, with, with our system.
Okay. Now. Interesting. And the interesting thing in the biological system is that somehow everything is packed together, right? Because, um, there is no, um, you know, no external temperature gradient that is applied in most cases. Um, and in fact, it is usually not temperature that maintains these fluxes from hot to cold, um, uh, to, to extract work. But there are chemical reactions going on that um, in principle generate the same, uh, picture. And there is an analogue to temperature gradient.
This is called the chemical potential. But all what that means is you have to, um, put energy into the system in a cell that's, um, nutrients, for example, that this particular cell you saw got from, from its mother. Um, and this allows it to, uh, so some molecular processes, um, uh, use these chemical potentials, turn it into work, turn it into forces. Okay. And this leads to all this fascinating, beautiful kind of self-organisation, um, that Julia and Adrian had, um, talked about.
Now, how is this molecularly implemented? I'm also here not necessarily have to go. And also because Adrian had mentioned this a few times and doing that as well. So if we look a bit closer at the surface of the cell, what we will see in the more simplified physics picture is a polymer network, um, where I sort of sketch these actin this, these, uh, uh, sticks here. They're called actin, uh, filaments, as we heard before.
And on these filaments, we have these very specific proteins called motor proteins that exactly do this fuel to waste conversion, um, by changing the confirmation of some, um, uh, molecules that are floating around, um, uh, and, uh, the is confirmation of change, uh, turns them from ATP into ATP.
Um, but the point is, if you have such molecules walking on these filaments and they pull on on one end and on the other, they are sort of naturally able to, uh, um, um, inject forces into this, uh, into this material. And you can also imagine that when I have a single cell doing this, and I have now a tissue where so many of these cells are connected, that these forces can permeate through the tissue and generate motion also on a larger scale.
And then you might find other mechanisms by which the strength of these forces can be controlled. And so what does this now look in practice? I add to the list of I hope you found beautiful movies that you have seen today. Um, it's, uh, organisms that we had seen before already. So this is, uh, zebrafish, very popular model organism. Um, and what you see here is the same process. Um, but it happens on the surface of a sphere. So we're looking on the left side from, from from here.
The movie on the right looks at it from just from the other side. But it's the same process. Each white dot here is a cell. Okay. You can think of this as a cell. And obviously each of these cells now is undergoing this kind of cell division that you saw in the first movie. Just the single cell doing. And then in the same time, they are moving around and coordinating their position in space and time. So it's a beautiful, um, uh, process.
And just another example to add to the list. Again, remember, we have a well-defined sort of molecular system in terms of what produces forces that sits in this case on the surface of an ellipsoid. Again, each dot here is a cell. And when we play this movie, we are looking groups. We are looking at the development of what is a flower beetle. And it has a kind of other, also an interesting geometry, but it's different than what we have seen before.
Actually, it makes a little compartment here. And later the embryo develops inside this compartment. So it makes all of its own, uh, um, uh, a cavity, uh, to uh, have to snuggle in and develop. So I just want to make the point. Right. So there are a lot of ways how these files can be translated into some very interesting, um, uh, morphogenetic, um, um, processes.
And so the question that I want to specify a little bit to what was asked before us, then, um, what can our physics actually, uh, contribute here to understand the development? Um, um, of of of of living systems. And I would alternatively titled this as maybe what's the condensed matter conundrum? Um, of of biology. And illustrate this with, uh, another model organism.
Yet this is the elegance single cell embryo on the left, fully developed organism here on the right, a sort of, uh, millimetre, uh, um, long worm. Um, half a million or a long one. Um, and it has, as an adult, about 3000 cells. And what's interesting to note about this, we know almost every microscopic detail of this, uh, organism we know precisely is a genome. Um, of course, from humans. We also know, uh, the genome nowadays.
But this was one of the first orders where this was actually fully, um, um, decoded. But we know much more than this. We know, actually, of all these 3000 cells that emerge in other organisms, exactly how they got there. It's very reproducible. We can follow and predict, uh, the position of of all of these 3000, uh, and a few cells on top of that, we know precisely it's neural network.
So it seems like we have all the microscopic information about this organism, uh, available from single cell to final grown adult. And still we have no, uh, close picture here. That was bring us from the single cell to to such a so such a picture as an emergent, self-organized process as we would think of this when when we look at it.
Okay. And I'm calling this a conundrum, the condensed matter physics conundrum, in a sense, because there had been a very influential, um, let's say, um, 50, 50 plus years ago, um, by Phil Anderson, who was a condensed matter that condensed matter. Um, uh, a physics non-equilibrium condensed matter physicist.
And he made this point in the context back then that, uh, some people were, uh, proposing that what, what needs to be done is to understand, uh, the fundamental interactions of nature, uh, say particle physics as good as possible, and then we know everything. Okay. And he was making the point that, um, this is not exactly true, but because as soon as you have many interacting units, you have something called emergence and collective organisation that's that comes out of this.
And you may actually have to think in different terms about describing these collective phenomena and are not able to necessarily derive them from the, uh, microscopic laws of your system. And that's where physics, um. Uh, of course, can really help biology because biology has the same issue. As I try to explain, um, uh, I'll convince you of with this, uh, ordinance on the top. And so what are the results then that that that I am, um, looking into.
So very bluntly. So I want to understand how a cell divides, how a tissue folds. And of course, when I say, how do they do this from my perspective, what are the physical principles that facilitate these, these processes? And then taking this together, um, how this can help, uh, an organism to, to develop as a whole. And suddenly I'm also a theoretical. I mean, I am a full time theoretical physicist.
Um, so what I really want to understand is what I can learn about these things using theories of of active matter. And then maybe more excitingly and also just this point, quite nicely, using biological systems to inspire our thinking about what theories of mass of active materials have to actually look like and what they have to be able to describe.
Okay. And so I just sketched essentially this last box here, um, on the, on the slide because it's really crucial as we've hopefully cooked up already, um, up to here, that this work is resulting always from very close interactions between experimentalists and theorists that, um, have very mutually fruitful interactions. Um, or when when is interactions are mutually fruitful. This is mostly where the most exciting and interesting things happen. And so this was kind of a general introduction.
So I want to now turn a bit more to what I, what I put into my title and want to tell you, um, what is reality. And maybe many of you have already heard about this, uh, for the purpose of this talk, what you have to think about it is think about an object that when you know it, it's just not the same object anymore. And this can be very nicely done. Of course, with hands we throw a hand. We have already we have another hand that is this metal, um, image. And clearly they can't fit on it.
Other if you sort of keep the, the orientation in the same way. And uh, another way to say that is, um, we have in this case a broken left right symmetry because left and right, um, and our body and in fact, in most organisms, um, is not the same. Okay. And you can already ask yourself this question.
If we start as a round cell, as an embryo that doesn't know a direction or front, a back up or down the right, left, uh, this must be somehow implemented because we end up all in a well-defined, um, with a well-defined morphology. Um, how is this symmetry breaking actually controlled and implemented in biology? That is why Kerala tea is in general a very interesting field to to to study in the context of facts matter.
Um, there are many more examples. I would really say that the living world as a whole is chiral. Um, I just as a few examples, you know, you can look at the patterns on shells and snails. You know, there are like spirals. If you think about a spiral similar, it's won't be the same spiral. You see spiral patterns in plants. Um, also more subtle. So this is a cross bill.
This is a bird that has evolved its beak to grow, uh, a bit more to the left on the top and a bit more to the right on the bottom. And it gives it this broad an edge over, uh, catching little backs out of, uh, narrow spaces from trees. Um, something I learned preparing, uh, this is this presentation. Um, and so if we want to link this a bit more to the research I have been doing, um, we have to get a tiny bit more technical where the reality is.
And the systems that that is interesting for, for physics. Um, and one aspect is the Acton we had heard now several times about Acton. Again, this all these molecules in the, in the surface of the cell, if you look at them a bit closer, uh, these molecules are built from, from monomers, but they are not built as a straight stick but as a little pitch whenever a new monomers edit. And so you end up with something that is more like a helix. Okay.
And the helix, just like a spiral, has sort of this notion of handedness in reality to it. So you have molecularly built into this cortex for reality. Okay. And then something I will get to later or a little bit more detail. This is the force generating, uh, structure. We had heard a lot about this. We haven't talked about um, I believe so far. Um. Uh, Celia. So I'm talking here about the thing about a sperm cell that must be propelled somehow through a fluid. So it has a little appendage.
Um, and there is a molecular motor machinery in this appendage, and it's very similar to the one that you see in the cell. The net outcome is that you have a machinery that produces forces that it exerts, then in this case usually on surrounding fluids and is sort of propels the cell or if you are stuck somewhere, moves fluid around. But I will, um, show you in a bit more in a few minutes, uh, a bit more details about this case.
So let's first look at what, um, this carnality here can do, can do for for cell. So remember. So what we are now looking at is again an embryo of C elegans. I just show you another image. Really these filaments are very clearly labelled in a specific way. You see this nice anisotropy, this sort of filamentous structure. So each of these white lines are essentially these purple and actin filaments.
And when these miles and motors are walking across these filaments, you get a very complicated dynamics. Because nowadays more myosin motors, they will pull and push on actin, move the cortex around. And that this gives you some sort of motion dynamics. So this is still a single cell. And we are looking sort of on the side of the cortex. So this is the single cell. Now the single cell has divided. So we are now we have now one cell here and we have one cell here.
This is after the first Division. And now something interesting happens. So it doesn't just divide anymore. It splits like everything we had seen so far. But if you look carefully when this movie starts playing, it will divide along this axis. Okay. This is not too, uh, not too spectacular, but it's actually also having motion in the top cell that goes farther to the right and motion in the lower cell that goes rather to the left. Okay, let's play this movie. Right.
So you have very significant motion that again has sort of this notion of helicity, of handedness of reality. Um, and uh, the indication is here that somehow this correlative of the action that I describe gets translated here through this act of processes into, um, a motion specific type of motion, um, of the, of the cell. And what you hopefully also notice is that the division axis as it divides, it is rotating.
So I start as a cell that essentially parallel to the left boundary of this, uh, video at the end it's somewhere lying diagonal. Um, in this video. Okay. And this is quite remarkable because at the beginning of the movie, you have two cells that sits along the line. That means all that this embryo at this time actually knows is what its front and its back will to be. But it doesn't know anything else. Any other direction looks the same up to this point.
Okay. But the moment you have this kind of division and this sort of rotation, you're selecting a specific plane and you actually finally broke morphologically left right, up down symmetry as well, the organism. So that's a very clear first moment where suddenly this organism starts to have not just the front and the back, but actually also the front. Uh, left right, up, down. And so this is the point I just wanted to make. And we looked a little bit more in detail. What what is happening here?
Um, what I want you to take away is there are cells that divide without rotating. Okay. So there are specific ways that we characterise this or the experimentalists characterise this. And there are cells that divide without um, uh, uh, tilting um, the axis. And the point is that this tilting of axis is very well correlated with having these counter-rotating flows that you will see on the,
on the surface of the cell. So this is what this plot is showing. So more comfortable attending flow basically goes to the left. And you see the more of this we have also the more we are rotating the cells. So there's a very clear correlation between flows and rotations and the physics here. The physics question is. What are the the talks essentially in this problem that translate. These flows actually rotate into the rotation of the cell.
And I spare you the details, but I tell you that what we arrived at after evaluating carefully how to talks balance in such a, in such a process, what we call the bulldozer model of cell annotations. And I'll briefly explain why. Um, so we arrived at a formula that says the amount of flow of this counter rotation is proportional to the rotation of the division axis. Okay. This is essentially what you saw in this plot. You had a more flow.
I have two more, um, rotations. So this comes out of the the theory. But the physics is in this pre factor here. And the three factors is what I have to look at is the friction on the two sides that this dividing cell, um uh, is in contact with the eggshell because it's particularly in contact with the axle on two opposing sides. And whenever I have a difference between these frictions, this this number will be non-zero. And I will arrive at something that will rotate in space, its axis.
And why do we call this a bulldozer model? Because a bulldozer that you want to rotate on a spot functions exactly the same way. Okay, so now the flows of the cell are represented by the motion of this chain. Okay. What I call here the two sides of the of the cell is basically the top of the chain and the bottom of the chain okay. And if a bulldozer stands on the streets, essentially the friction is infinite with the street and there's no friction on top because just nothing on top.
And you see, you in this case, in this limit, this just becomes one. And I'm perfectly translating the motion of this chain into a rotation of this bulldozer on the spot. And it's this same principle that this cell now exploits to convert molecular chirality of the actin into chiral cellulose, into a rotation of the cell axis, which ultimately, for the first time, breaks morphologically the left right symmetry of this organism.
And so now I move to the sort of second example of, of my research I had mentioned. There's this other very interesting force generating structure in biology called the Syrian. Um, the, the types of molecules and motor protein involved are different, but they are the same, same principle. And where's the reality here? Well, if you take a cross-section through this Syrian, what you will find is molecules arranged again in the kind of helical structural way.
So, uh, this, this, uh, arrangement here is called the axon. And this goes through the whole flagella. And it also has a pitch throughout. So there's an inbuilt reality as well into these and archaea. And I'm not interested so much in a single column. But actually what you have a lot in biology are what are called cilia carpets. So those are structures that have different kinds of functions. Um, but they are structures where you have many, many of these beating cigar together.
So they are all very densely packed and form these kind of carpets. So what we have now is a surface with a lot of cilia that beat. And keep in mind now this beating will have some chiral nature to it. And in what context? Um, ten. Something might just be relevant or why at all? Um, you know, we think this is important to, to understand how these topics are affecting flow and vice versa. So it is a very, um, interesting condition called CTOs and vassals.
For anyone of you have not heard this before. So about one in 10 to 20,000 people among us have a completely mirrored internal body plan. So essentially all organs, everything is perfect. It's not just on another side. The whole morphology of everything that's internal is mirrored. And many of these people live a healthy life, um, and don't even notice. Um, but what has been found is that this is often related to a specific gene mutation in human, um, that codes for making cilia.
Okay. And so the idea is here that at some point in the development, the CIA will be used to generate some kind of flow that, you know, pertains to tissue. And if this flow goes in the wrong direction downstream, when you arrive at the, uh, the new pond you have produced, um, uh, um, a human being that has a completely internal, uh, qualified. Okay. So we go a little bit more. Lo lo lo lo lo fi. Um, and look at, uh, um, starfish embryos.
We had seen those already. Um, so because what they, they also have clear cockpits, but slightly different purpose. So this is a microscopic image where you see each of these little or what looks like threads that come out, they're all clear and they just keep beating on the surface of these little embryos. And what this does, it allows these embryos to swim. Okay. Of course, this doesn't look anything like a starfish.
This takes quite some time to get there. It's really we are just looking at this early stage where it's somewhat benign ellipsoid. But the point is it can swim. And what you maybe can see already in this movie is it's not just swimming, it's also rotating. So it has the forward motion, but also a corkscrew aspect to it. And what we got interested in here is that these embryos not just swim, but they also quite often, uh, approach the surface of the fluid between the fluid and the air.
And then they don't really swim, but they just keep rotating so that they, they maintain their rotate, the rotary aspect of the motion, but they don't really swim away anymore. Okay. And what was particularly cool is now if you put a lot of these embryos together, a lot of them come to the surface and they make these amazing, uh, what we termed living chiral crystals. We call them characteristics because this rotation direction here of this embryo is every time is always the same.
So you don't have some spinning right, some left, it's always the same. And of course suspicion why it's always the same is again, because, you see, I have a hard coded handedness from the molecules that build from and accordingly, this rotation is also hard coded. Um, by the way, uh, and due to the fashion they are make themselves swim. And the idea was of this project not so much necessary to understand what's the biological meaning of this crystal formation.
But really, we thought, this is a great opportunity to study two atoms of physics, because we have very good access to understand these embryos, how they are moving in the fluids. And so the question is, how can we understand from their properties what the properties of this emerging crystals would be? And if they are different from crystals that we are used to? Okay. And one way to, to do this, of course they are in the fluid.
So we want to understand how the food around them moves. What you see here hopefully in this movie is they're little particles around. So it's a bit um, there's some, some uh yeah, some structure. These are little bits that are also put into the fluid. And the assumption is now that these beads move, uh, like the fluid does. So that means if you track the velocity of these beads, you know how the fluid moves in the surroundings. So this is called, uh, particle image velocity of the tree.
And if you use that, you can get a map like this that tells you regions where the flow is very fast and regions where the flow gets slower. And so naturally it's fast close to the embryo, it's get slower moving, moving away. But what's more important is that it's now giving you immediately an idea of why at all there would be a formation of these crystals, because this fluid, what you see is it's drawn into the embryo from all sides.
Now imagine you have another embryo sitting here. Naturally, it will sort of be drawn to this one embryo as well. And all of these embryos are doing it. And so naturally you have a mechanism to nucleate, um, uh, these kind of, um, a chrysalis. And there are actually also other biological systems, um, whatever that specific algae, um, that has a similar, uh, flow, a phonology, um, that was studied in Cambridge and in quite some detail some years ago. So this is a single embryo.
When you want to understand crystal formation and the properties of a crystal, you need to understand a bit about how these embryos are interacting. And the simplest interaction that you can have is in a pair. Okay. And essentially one important thing that is happening is not just that these embryos independently spin, but the moment they come close to each other, they start, um, dancing around each other. So they're orbiting around each other.
And qualitatively, the reason is that between them there is still some fluid, but because they are so, so much nearby and both want to rotate. Um, the kind of talks and forces that emerge, hydrodynamics, make them, um, uh, walk, uh, around each other. And studying this problem quantitatively in more detail. You can come up with a theoretical model of this process that captures, and in many ways, the kind of crystal formation we see in experiments. Now imagine this is the top view. We have disks.
They are following the interaction rules that we have determined from the kind of experiments that I just shown you. Um, and the colour code here is the rotation frequency of these embryos. And one thing maybe to note, you see that they slow down quite a lot. Yeah. So they start at a rotation speed that you see by I hear a single rotation of an embryo. And the final crystal takes about three minutes. So you don't even see anymore that they rotate, but they still do rotate.
And that's some nice observations that you can check that sort of to, to test your intuition in a way. So what I showed you here is the final state. The colour code again is the amount of rotation the speed of rotation. One thing, we immediately see that the, um, boundary embryos are usually faster. That's not so surprising. Okay, so those are embryos that have less neighbours. So in a sense, they have a they have a less hard time to rotate because there's less to work against.
And this is something you will find also um, in the experiments. So you see these boundary embryos rotating much faster. You don't really see their, their rotation. Um, those ones are much slower. But then interestingly, there are also some fast ones in the middle, so you see some very bright ones here. If you look at the theory, what we find is that those are ones that are rather on the smaller side also makes sense.
They have less contact with the surrounding, so it's easier for them to keep rotating. And that's also something you see in experiments. So here's one mark that is a bit more small, a bit smaller. And you see it's going quite, quite wild. Um, whereas the other ones again in the surrounding do the usual um, rather relaxing spinning. And then finally we have the opposite thing as well. Um, we have some here that actually rotate in the opposite direction.
Okay. And if you look carefully, what is happening is you have some of them that are really they are large, statistically speaking large. And at the same time, they don't want to spin themselves too much. Now imagine this embryo in the middle doesn't want to spin at all. And all that happens is that the neighbouring ones are at full speed spinning. Okay, if you look at the interface, what they will all do. They will spin in a one in the opposite direction that is usually turning.
Um, and this is something we see in experiments as well. So we have two examples of two pig embryos. And you see that they spin precisely the opposite direction of, of what other embryos, all other embryos doing. And so this gives us a little bit of a sense that, that we are capturing most of the physics here. Um, uh, in the right way. And so finally, what was about to kick off this project? This is sort of microscopic, how I describe the system now.
Um, but we were wondering what what are some of the macroscopic properties of this crystal? Okay. So we know that, uh, you know, uh, condensed matter solids, uh, solids, um, a range of known crystals. We can think about their, um, emerging, uh, uh, material properties. Can you say something similar about these kind of crystals? And when we look at our theory in more detail, we found, um, quite a surprise.
So back in the, um, continuum mechanics, uh, courses that that we take, we are usually told that for such an isotropic solid, all you need is two material parameters to describe all its properties. Okay. And Adrienne mentioned this, um, and that is, you know, uh, usually true. But what we found is that, um, our crystal somehow requires four parameters to describe in full all its elastic properties.
So we are very carefully going back to our introduction to solids courses inspired by by my daughter. Um, and we found actually it's not a problem at all. The reason that this is allowed here is that what you what one is told about this two parameters also assumes that the system is at equilibrium, okay? And our crystal is not at equilibrium. We have living organisms that are pumping constantly energy into the system.
And as a result of this, of morality and non-equilibrium nature, we are allowed to have these additional material parameters. And actually, um, they are referred to as elastic parameters. And this was a theoretical concept that not so long ago was, um, worked out by a group in Chicago with some beautiful physics that we could kind of find again in these, uh, living crystals. And then. So just finalise and end with two slides of some exciting movies and dynamics that is Christmas.
Also take all the consequence of its complex properties. They spontaneously oscillate. So this is this for the crystal, and I hope you can see that there are some sort of large scale displacement waves that are travelling through this crystal. Um, uh, that, that we observed and normally again, in a normal conventional crystal, this this would not happen because this is an over time system. It's a very small length scale.
But here the activity injection, this is sort of a data processed version of this um, allows these displacement waves to spontaneously pop up, uh, in these um, uh, in such an overtime system being a consequence of its non-equilibrium nature and being a consequence of its reality. And with that, I come to the conclusion. Um, I hope I could convince you at the beginning that active matter theory is a really powerful tool to study, uh, complex phenomena in biology.
Um, that I showed you that chiral cortex flows, uh, translates through fiction into some morphological left right, some breaking. Um, and finally, um, I told you about these, uh, new living crystals that we found that have some conventional, unconventional, elastic properties.
And I really want to thank, uh, specifically the people that were involved in this project that I talked about, uh, excellent collaborations with, um, uh, location, um, and, uh, the faculty group at MIT, um, and, uh, for the lab and your technical supervisor at MIT. Um, but then also, I want to thank the, um, Rafael Centre here in Oxford, uh, for being absolutely amazing, um, colleagues. And I'm happy to take any questions. I don't have postdocs to take the nasty ones, so.
So, please. Thanks. Look.