 Hello, and welcome back to this little mini-series on how and why to model developmental systems. I've tried to sort of convince you in the first lecture in this mini-series that you need dynamical models to get at a mechanistic explanation of any developmental process. So it's not enough to just take it apart using genetics and molecular approaches, but you need to put it together again using a model to truly understand it and to provide a causal mechanistic explanation of how it works. As promised, we'll continue by illustrating this sort of principle with two examples that I think show really nicely how modeling contributes to insights that you cannot get through genetics or molecular biology and also illustrate I'm coming from an evolutionary developmental biology background. Illustrate the second point of this lecture and that is that sort of the comparative analysis of developmental systems is extremely important if we want to distinguish between the accidental features of the system and the actual design principles come back to that a little later. So this first example here will be a vertebrate based on the vertebrate limb, its development and its evolution. So we're looking at the fin to limb transition because it's an absolutely beautiful system that's very well documented in terms of its developmental biology and also has a very good sort of fossil record in terms of evolution. For example, you have a lot of these intermediate forms like this fish, tiktalic, a fossil that was discovered by Neil Shubin and colleagues and is mainly famous as being the fish that can do push-ups. So what you see here is a sort of a sarcoph, the ridgian fish fin, a tetrapod limb and this beautiful fossil here has a fin with a wrist so you can push. So what's interesting about this transition is it's well documented. We understand a lot about the development of structures but there's still a lot of open mysteries and very important questions. For example, look at a phylogenetic tree of the vertebrates here and at the base, basically branching here you have the chondrichtius. Among them the elasmobranchs are the sharks, the rays and the skates and they have a fin structure that looks like this. Here are the proximal elements, distal sort of fins, fin rays and that's important. You have an anterior protopteridium, sort of a mesopteridium in the middle and the metapteridium in the posterior that you can distinguish. Now, if you compare that with the fin of a bony fish, the tiliost fish, it's completely different. Particularly, these distal elements of the bony fish fin are very different bones from what you usually see in a limb. They're derived from dermal tissue, they're completely weird, so probably derived and they are attached to the shoulder in sort of a part that looks like this, the protopteridium, sort of the anterior of the shark fin. In contrast, if you go all the way up here to the tetrapods, you have a very different structure. You have a stylo podium, femur, humerus, the proximal part of the limb, sugo podium, ulna radius and then the autopodium, for example, your hand, your metacarpals, the digit bones, the phalanges, et cetera, out here. And the sort of conventional wisdom is that these proximal parts are sort of conserved. You can look at the way that the sugo podium is attached to the stylo podium and you can reconstruct that it must correspond to the metapteridium of the shark fin while the autopodium, the hands and feet of tetrapods are widely believed to be an evolutionary innovation that has no equivalent in the shark fin. So let's sort of examine that problem in light of the development of the vertebrate limb. And that brings us right back to the French flag model. So here are a few examples, first of all, of vertebrate limbs. Just within the tetrapods, you have this absolutely amazing diversity of a human hand. Here's a gecko, some sort of lizard, a cat, a whale fin, a bat wing, a frog, a forelimb, and a bird wing, completely a huge variety, but clearly they're all sort of variations on a theme. The coloring scheme here shows the homology relationships of the different bones and it's not difficult to reconstruct that. So to understand this sort of variety, we need to understand the theme on which the whole diversity is based. And that theme, of course, is the developmental process that creates the vertebrate limb. And that brings us back, as I promised before, to the French flag model, which is a classic sort of model for limb development. And it says that the different digits of a vertebrate, a tetrapod limb are patterned by a gradient of sonic hedgehog morphogen that emanates from the zone of polarizing activity here at the posterior of the limb bud and forms this gradient across the limb bud, which is interpreted by the cells, which then turn on different differentiation genes that lead to different digit identities. But this is hotly debated. There's an alternative view that was proposed by Alan Turing, which is a much more self-organizing way of producing stripes. That was for a long time seen as some sort of competitor view to this French flag model. And a lot of sort of experiments and whole research programs are designed to distinguish between those two different alternatives. So let me explain a bit more what Alan Turing's model is about. We'll go into a little digression away from limb buds. And we go straight back to 1952, when Turing, who was the father of modern computers, he was working on computing theory and information theory and all kinds of branches of mathematics. And so this is his only paper in the field of morphogenesis and it completely turned the field upside down when it was published. It was revolutionary. So what Turing did is he took a simple system of two diffusing substances, which he called morphogens, that interact in certain ways. And he showed for the first time that these morphogens could form patterns. Can you see the only figure from his paper here? And it's just a bunch of black blotches and a white background. But the revolutionary insight was that diffusion could act as a mechanism for creating inhomogeneous pattern. Before Turing's paper, everybody thought diffusion was the thing that made us able to breathe in a room. Like, I'm in this room and there are air molecules everywhere because of diffusion. They're not all bunched up in the corner up there. So diffusion was seen as a sort of a homogenizing influence. And Turing here turns this upside down and shows that two diffusing chemicals can generate pattern in homogeneous pattern from the perturbation of a homogeneous initial state. So you get diffusion-driven symmetry breaking or diffusion-driven instability in mathematical terms, which was a completely revolutionary insights both for physicists and for biologists at the time. His paper is a beautiful illustration of what good modeling looks like, okay? So it's called, it's sort of, here's the citation record of it over time. And this type of paper is called a Sleeping Beauty Paper because you see it's published in 1952 and then up to 1970, almost 20 years later, it gathers almost no citations. I think it has about 17 citations by then. And then modeling, theoretical biology comes up in the 70s, modeling, and then systems biology here, and look, it takes off and by now has hundreds of citations. So this, I want to point out, is exactly what good theory should look like, okay? It's well ahead of its time and it does something revolutionary that's not recognized until much, much later when the experimentalists have called up. Now, this is also a career killer in today's idiotic system that's based on short-term productivity and gain, okay? This is why theoreticians are driven to extinction, especially good theoreticians like Turing wouldn't get a job nowadays in this stupid system that we've created, end of rant. I'll come back to the experimental side again here. So in the 1970s, we saw this in Turing's sort of citation graph. It starts taking off and in particular, what's happening is that Hans Meinhardt and his collaborator, Geer are proposing this specific instance of a Turing system without knowing about Turing, by the way, at the time, so they reinvented the wheel, basically without knowing it. And it's a classic Turing system nowadays. It's much more realistic in terms of the biological sort of application. So it consists of two morphogens. Again, one is an activator that activates itself, but also an inhibitor which represses its own activation. So this seems paradoxical, but what you need to know is that the activator is diffusing much less rapidly than the inhibitor. And what you get is you start from a homogeneous pattern. Homogeneous, here's a tissue, one end, the other end, and the concentration is homogeneous. And there's a little fluctuation. You can see this here in the production of the activator and the different cells in the tissue. So what's happening is that in some region of this tissue, there will be suddenly a bit more activator than in others. And so it activates itself and so it creates more and more of itself, but it also activates the inhibitor, okay? But since there's a lot of auto-activation already here, the inhibitor is not able to overcome it while since the inhibitor diffuses more rapidly than the activator out here in this end of the tissue, it outcompetes the activator and you get this beautiful gradient-like on-off pattern across the tissue, activator on, activator off here. If you tune the diffusion rates, you can get more fine-grained patterns. So here is either a larger tissue or a more closely spaced tissue and it will form stripes of coinciding stripes of activator and inhibitor. So here the pattern is generated. Again, that's very important through the difference in the fusion rates between activator, slow and inhibitor fast. So it doesn't depend so much on the precise interaction scheme of those two factors, but on the different diffusion rates. And those diffusion rates that give you a pattern like that, that's called the Turing space. We'll come back to that. So these models can give you just like any other model, they can give you all kinds of different patterns. So here's a beautiful illustration from a review by Kondo and Muren in 2010. So most of the time, just like any other model, I have to repeat that again. It doesn't give you anything. Homogeneous pattern stays homogeneous. Nothing happens. Sometimes it just oscillates across the whole tissue or then it forms these very sort of short range patterns. And sometimes these oscillate. So this looks like white noise and then this looks like white noise on your TV. Salt and pepper, not very interesting, but these two last cases are interesting. So you can get case number five, you can get oscillatory waves to travel, for example, here like in a dikterstilium slime mold colony when they aggregate or the famous Bellus of Jabotinsky reaction that forms these rolling spirals and waves in a dish. Beautiful experiments. You should Google that and look it up. But the most interesting case for biology are these stationary waves with finite wavelengths. Case number six here, they can form all kinds of stripes and spots. These sort of Turing systems are an extremely versatile pattern generator. This is demonstrated by a fun little paper by two Polish authors who wrote the alphabet in Turing systems. Okay, this is not just a joke because for example, you can, if you look at butterfly wing patterns, you can find the entire alphabet and all the numbers of those wings. Just look closely at that. And people do use Turing systems to explain pattern formation on butterfly wings. Beautiful book here by Hans Meinhardt in the fourth edition, the algorithmic beauty of seashells. So he took seas snails mainly in clams and simulated the amazing patterns that you see on their coast, which are not adaptive because these animals are actually buried in the sand but they arise from the particular growth mechanisms and growth patterns of these shells. So this is absolutely gorgeous, gorgeous work. Or animal coat patterns, of course. Here you have some sort of a giraffe. I love the work of Sarah the Ramer. If you visit her website, she has all kinds of weird animals that she creates, impossible animals, beautifully bizarre creations. So this was one of the first applications of the Turing system here by Jim Murray. In 1981, a model that simulated a Turing system on a sort of a realistic coat pattern of an animal, although it looks more like a safari trophy. To me, very abstract one. And again, if you tune the shape of the domain influences the pattern, but if you tune the diffusion coefficients you get from these simple sort of on-off patterns, the very intricate spots and stripes. This is not just theoretical here. There's a mother tapir with her baby and you can see the tapirs are basically walking and growing Turing systems. The baby has this very fine grained pattern of stripes and dots in the mother, just this very large scale, black and white pattern that you can simulate using a Turing system. So Murray looked at that as well. So he simulated his system on growing domains. So you can either change the diffusion coefficients of the size of the domain and the shape of the domain in which you form the pattern. And a paper that I really love here from 2017, very recent. What they did here is they took different lizards and they scammed them using a geographical information system. So they created a realistic three-dimensional lizard pattern and they simulated Turing systems on those patterns and showed that the body shape of those animals is greatly influencing whether they will exhibit spots or stripes, so the size and the shape, the growth patterns of these animals determine the code patterns, beautiful work. So, but Turing, during his lifetime still, he wasn't very impressed with this. He said, probably, we're not quite sure, but it would be nice if he would have said it. He said, talking about a zebra, he said, well, the stripes are easy to do. But what about the horse part? The really interesting stuff is the horse part, which brings us nicely back to our initial sort of motivation and that is to study patterning in a vertebrate limb. So I'm gonna present some work that came out of Jane Sharpe's lab in Barcelona. This is a beautiful paper, 2014, by Yelena Raspupovich and also the channel Mark Ham where they, so what they did is they took the vertebrate limb butt in a mouse and reconstructed, not only its growth pattern, very, very meticulously, but also projected the sort of expression patterns of different genes onto that growth pattern. The result can be seen here. So these are different mouse limb butts of different embryonic stages from E 10 and a half to E 12 and a half. And you can see there is a sort of a changing pattern of expression of this transcription factor, SOX-9, that comes to resemble a pre-pattern for the digits at the end of this process here. So you have a stripe of SOX-9 for each digit that is going to form later in development. So what they did is they took this very, very realistic growth map of the limb butt that they had and simulated a Turing system on that shape. And what they got was stripes, but you don't want to have fingers like that, right? So they're crooked, they're sort of bifurcating, they don't look like fingers at all. So this is a problem. So obviously, so this is one of modeling strategy. You put in sort of a minimal system and you see if it works. If it doesn't work, you add additional factors, right? So there's a second, so there's an additional factor here. They took a HOX gene, HOX-D13, which was observed to be co-expressed exactly in that domain that forms the digits in the actual mouse length. So you can see the expression patterns here of HOX-D13 and the simulation that includes them is already much more similar to what you see here in the actual embryo. But still you have bifurcated limbs, they're crooked. You need straight stripes and no bifurcations. Another factor that's expressed in this limb of the mouse is the morphogen FGF. And it forms a gradient emanating from the apical ectodermal ridge here inward towards the proximal parts of the limb. And so if you include this in the model, but not HOX, then you get straighter, less crooked stripes, but too many and also splayed like this so that they are not straight in the sense that they don't point in the right direction. So what you need to do is you need to have this sort of core system including SOX-9, wind and BMP and you need to have both HOX-D13 and FGF signaling involved and then you get a beautiful pattern that closely resembles the expression pattern of SOX-9 here. Now the interesting thing is you can analyze this model and you can show that the way that HOX-D13 and FGF influence this is by modulating the parameters. So the strength of the repression of wind and BMP by SOX-9, these different parameters, K7 and K4, if you tune their strength through the action of HOX-D13 and FGF, what happens is the following. If you analyze the system, remember that I said you only get Turing patterns with certain parameters and you can show that as you go from the proximal limb here, more distally, you enter this sort of Turing pattern in space here. This is what it's called and this is the explanation of why you get a Turing pattern only in the distal part of the limb. Okay, so the model doesn't only give you a realistic pattern, it also gives you hypotheses on how these sort of factors need to interact over space and time and how these interactions need to be modulated precisely to get the pattern you want. Okay, and this is impossible to get by just decomposing the system using genetics and molecular biology. So now we have an interesting sort of hypotheses here what's especially interesting is this role of FGF because, oh, before I explain that, let's look at a movie of this model because it's beautiful. What you see here is the limb is sort of growing, the red domain is HOX and the green is FGF and the white is the SOX9 pattern that emanates in the distal part of the emerges in the distal part of the limb. So this whole, the role that FGF plays here reignited this whole discussion about whether the limb is a French flag or a Turing patterning system. And it turns out it's both. Okay, so these are not alternative views of explaining patterning in the limb but they're complementary. Only with modeling can you resolve this issue. Okay, you cannot just do experiment. And so what the model shows is that what FGF is basically doing is it's tuning the parameters to adjust the spacing of the different stripes which is what you need to get this sort of straight sort of pattern here because otherwise remember the stripes are crooked and bifurcating as to the main group. So basically FGF forms a gradient just like a French flag and it is tuning the wavelength of these different stripes which leads to the stripy pattern. So what you have here is a French flag type of system interacting, complementing with a Turing auto regulatory self-organizing system to create these beautiful robust and regular stripes that the formula is. Okay, so we know this about the mouse. This is a great step forward. It gives us a new view. It reconciles to apparently contradictory views but what about evolution? So let's look back. I said there's a beautiful fossil record. You can see the mouse limb here on the right. And if you go back, you have a bunch of intermediate fossils and the dogfish here. And what is indicated here in red is our sort of the distal elements of these different structures. And from looking at it, you can say nothing, right? I mean, they have no resemblance to each other. They're not the same in shape, number. You don't know anything. You don't know whether these distal elements in a shark fin correspond to the autopop in the mouse or whether this autopop, the hand, is really a true evolutionary innovation. And this problem was resolved by beautiful work by Ko and Imaro in Jane Sharpe's lab. And what Ko did is he's a very patient man. He studied the embryonic development of dogfish. Their eggs are beautiful. Mermaids pouches, they're called, they're translucent, beautiful structures. But they take an awful lot of time to develop a month to go through these different stages. So Ko mapped the clonal analysis to map the shape changes in these shark fin limb butts and also mapped the expression pattern, for example, shown here for Sox9 onto this butt. So you have an early distal proximal pattern here. And then later on, you get this distal sort of pattern that resolves into this row of dots here, but not quite at the distal end of the fin but somewhat removed from it. So Ko then went on in collaboration with Lugano Marcon and applied the mouse model to this different shape of dogfish limb butt and also mapped to different expression patterns of the elements of the model. So here's a Hawks gene, Hawks A this time, Hawks A13. And it's different than in mouse. You can see the Hawks gene is expressed in a domain that excludes the expression, Sox9. In the mouse limb, they were coinciding. And also they had some difficulties reconstructing the pattern of FGF. You cannot stay in FGF directly. So what they did is they simulated a gradient pattern based on the expression of a known target of the FGF morphogen called dusk six. And what they did is they took these data and they modeled the same Turing system as in the mouse on the dogfish sort of shape and expression patterns in the limb. And you can see the model forms this beautiful, realistic series of dots, okay? But there are some way away from the edge of the limb. And this is because in this case, as you go from proximal to distal, you go through Turing space. So you enter Turing space exactly where those dots are farming, but then you're pushed out of it on the other end. So the model produces other gene expression patterns as well, BMP and wind with these very sort of close, closely spaced dots. And what's even better, you can make predictions with the model, okay? So you can say, if you have more or less signal, this sort of space where the pattern occurs should be shifted, okay? So the model predicts that if you have a strong signal, the pattern should be further away from the distal tip of the fin bud than if you have a lower FGF signal. And you can apply a pharmacological inhibitor of FGF to the limb bud and experimentally show that the distance of this dotted pattern diminishes from the distal end of the fin. So this is absolutely fantastic work in a non-model organism, a model of this developmental process that you can compare to the mouse. There's some experimental confirmation, beautiful. So what does it tell us? It tells us that these two different distal shapes represented here by the pre-pattern of socks line in dogfish and in mouse. Nothing in common, right? Are they homologous? We don't know. Well, the model seems to indicate that they're generated by exactly the same Turing system in a different genetic and geometrical tissue context, okay? And so the model, the same model gives you very realistic sort of reproductions of what you see in the actual embryo. And you can explain how the two, the same sort of theme varies in both of both animals. So in this case, you have a model that sort of goes through Turing space in a very localized area forming this very narrowly defined row of dots while here FGF is modulating the system in a different way to modulate the wavelength and you get this blade digit pattern. Okay, so these two structures very strongly suggesting are homologous to each other because they're based on exactly the same growth process. Okay, so this is an amazing sort of insight that resolves a 50 year old debate in the evolution of development. But of course, Turing patterns not only occur in limbs, they occur very important for left, right to symmetry in vertebrate bodies and they form feather patterns in birds. Our hair follicles are formed by a Turing type systems, the branching patterns of our lungs and also rugae, which are the structures when you put your tongue on the top, the roof of your palate. You have little, there's a little rugged sort of structure and these are the rugae and in mice there's a beautiful Turing system model that shows that these rugae are formed by a self-organizing pattern generator like this. Okay, to summarize this example, Turing systems generate patterns, spots and stripes through the differential diffusion of two interacting morphogens, very important. The stripes are easy, what about the horse part? Vertebrate limb development involves both Turing and French black kind of pattern, beautiful model by James Sharp. The same Turing pattern generator positions distal limb elements and sharks and tetrapods, therefore these distal elements are probably homologous. Our hands and feet are not evolutionary innovations, they're just very derived structures that are built on elements that are already present in shark fins and the model on covers that seemingly dissimilar patterning processes are variations on the same theme. So if we truly want to understand how evolution shapes the developmental processes that in turn shape our bodies, modeling in this data-driven kind of way will be absolutely essential. Next time we'll finally talk about flies again. I'm sure you couldn't wait. If you have questions, contact me. Thanks for listening and I hope you tune in again next time. Bye now.