 Hello, and welcome back to this mini series about why and how to model developmental systems. In the first lecture, I sort of tried to motivate why we model, we model to get a mechanistic understanding in the sense that we have not only to take a developmental process apart to identify its components and their interactions, but we also need to understand how they lead to an organized behavior of the developmental process. So you not only have to take the system apart, but you have to also put it together again. The second lecture, we looked at the example of vertebrate limb development and the fin to limb transition to show you how a model can give you new insights into the pattern forming process and its evolution. And in this lecture, I want to introduce one of my favorite sort of systems because it's based on my own work on the function and the evolution of segmentation genes, especially the gap gene system in different species. So we're going to move back to insects and start this lecture just like the first one with the vinegar fly, Drosophila melanogaster, classic genetic model system. In the first lecture, I also introduced the segmentation gene network of Drosophila already. So if you're not familiar with this system, please go back and watch that lecture. And we're going to focus in particular on this first step of the casting where these maternal gradients, long range gradients, transcription factor gradients, it boosts the expression of broad overlapping domains of gap genes and these combinations of gap genes that are expressed form different territories of gene expression. So historically, this is seen as a classical French flag sort of problem. But I also told you in the first lecture, the French flag is a kind of a static system, a static way of looking at the problem. So we have to refocus on the developmental trajectory, the dynamics of the whole process. I was showing you Waddington's landscape arguing that what we want to know is that the geometry, the shape of the trajectory, the developmental trajectory, this is what it means to understand development. So what do I mean by that? I want to illustrate these very abstract ideas with a concrete example. So let's start simply here. What I'm going to do is I'm going to look at the interaction of only two gap genes in the embryo. You see a fly embryo here, the anterior is to the left, posterior is to the right. It's in a sensational blastoderm stage starting to undergo cellularization. Each dot here in the picture is a nucleus, and what I'm showing you here is an immunofluorescence staining of two gap gene products, the expression pattern of crouple in green and giant in blue. And what we want to do is we want to understand how do these genes regulate each other to bring forth this sort of beautiful pattern that we see in this picture. This is called reverse engineering, a developmental system. Okay, we're looking at it and we're trying to find out how does it actually work, instead of breaking it like we do in genetics and decomposing it, we try to understand the behavior, the organized behavior of the whole system. In this case, of course, I'm bringing up this example because it's pretty simple. You can look at the patterns of these two genes and realize that they never co-occur in any of the nuclei in the embryo. So either a nucleus is expressing crouple, it's green, or it's expressing giant. It's blue, but never both at the same time. So we can infer from that, these are two, remember, two transcription factors that can diffuse because the embryo is not yet cellularized. And so we can infer from this that crouple and giant really, really hate each other. Okay, so they strongly repress each other. And that leads to this sort of toggle switch behavior where a nucleus either expresses the green factor, crouple, or expresses the blue factor, giant. So we put this in a spatial sort of context and you get this beautiful pattern that you see in the middle of the embryo. Of course, the situation is a bit more complicated here in the head. We're not going to go into that right now. So what we've done right now is we've reversed engineer developmental system. We looked at a pattern. We inferred the regulatory network that produces this pattern. And we sort of mentally simulated how this could happen because it's a very simple system. But most systems are too complicated to do that. So we need to build up some conceptual tools, concepts that help us describe what's happening, the dynamics of what's happening. So what I'm going to do is I'm going to take you on a little five minute trip into dynamical systems theory and its concept. Fasten your seat belts. This is going to be a very quick tour. So to understand what's actually going on, to understand the behavior, this toggle switch-like behavior of the system, we can use a very, very powerful mathematical tool which is called a face portrait of the system. So what I'm doing here is I'm drawing an abstract space. It has two dimensions and each one of those axes that it has corresponds to the concentration of one of the two factors. So down here is the concentration of the blue factor x or giant. And on the y-axis here is factor y or crouple in green. Okay, so the higher up you go, the more to the right you go, the higher the concentration of these two factors. And you can start simulating this very simple system and look what it does. And so you will start somewhere within this abstract space, which is called the face space or the state space of the system. And the system will then follow these sort of arrows here, you see. It'll go quickly if the arrows are large, slowly if the arrows are small. And so if we start here, for example, with more giant than crouple, the quite low concentrations, it will move up here and then slowly go down here. So these arrows represent the flow of the system. To understand what a system does, we need to understand its flow, which determines how it changes in different circumstances. In particular, if we start at a specific point, we get a specific trajectory. Okay, and it has the specific shape in this abstract space. Here it goes quickly to this region and then very slowly out here to this blue point. This is a special point. And of course, the shape of this trajectory here has a lot to do with sort of Waddington's developmental creos and their shape. So these two blue points, which are at the end of most of the trajectories in the systems, they're called attractors. So when you follow a trajectory, you will usually end up with one of the two attractors. One of them has a really high concentration of giant and no crouple. The other one has a really high concentration of crouple and no giant. So here is the toggle switch behavior. No matter where you start, more or less, as long as you start with a little bit more of one factor or the other, if you start with a little bit more crouple than giant, you will end up up here. Lots of crouple, no giant. Or if you start with more giant and crouple, you will end up here, no matter how high the concentrations are. What really matters is only the difference between the two factors. So these attractor states determine the toggle switch behavior, either crouple or giant. That's it. These are the only two attractors of the system. The first thing about these attractors is if you push the system away from them, they will return to it. There's a third steady state in this system, which is called a saddle. If you start in a noiseless system without fluctuations, exactly with the same concentration of crouple and giant, you will follow this middle line here until you end up with the saddle. But this is not a stable steady state. As soon as you fall off this line, just by a little bit, you end up with one of the stable attractors. This is called a saddle point, and we'll see in a minute why it is called that way. The saddle point sits on this special line, the separatrix, between two basins of attraction, because we saw that no matter where you start in the green or the blue triangle, you end up with one of the attractors. So each attractor has an associated basin of attraction. So the geometry of the phase space that we've seen here, not only explains the toggle switch behavior of the system, that it will go either to high crouple or to high giant, but it also explains why it will do so robustly. Wherever you start, as long as you have more of one factor than the other, you'll robustly end up with one of the attractors. And just before we move on, there's a very special feature here. If you move straight from the saddle to one of the attractors, there's this value of very slow sort of small scale arrows. And this is called an unstable manifold. Now there's another way of representing this sort of abstract space, phase space, and that is if we interpret each one of those arrows as sort of a slope in a landscape. Okay, so what you can do is you can project this picture into a three-dimensional space where each arrow represents the steepness of the territory. And of course the attractors are the lowest points in the system. And you can see now why this point in the middle is called a saddle point. It looks like a mountain pass or a horse saddle. And basically you have two steep slopes that lead to the middle here and then two valleys, the unstable manifolds that go out from the saddle to these attractors. Okay, so does that remind you of something? Of course, what we've done for this very, very simple system is we've made the metaphor, remember, Waddington's landscape is a metaphor, not a model, but we've now made this metaphor precise in this abstract phase space. So what you see here is nothing else but a Waddington landscape that is read out of the expression data, of the expression dynamics of these two captions that we were looking at before. Of course, the real world is more complicated. If we add more factors, this landscape becomes more than three-dimensional, which is difficult to visualize. That's why we took such a simple system. And also the strength of the interactions between these genes can vary over time. That's what we said the last time. And also, so this can happen during developmental timescales, but also over evolution. So what evolution is doing, this is Waddington's second most famous depiction, is it changes the shape of the landscape. So the landscape is thought of as being connected through this very complicated network of ropes to these pegs here at the bottom. And these pegs represent the genes. If you change the genes through these very complicated interactions, that's the genotype, phenotype map, they will affect the shape of the landscape. And if you can understand the change in the landscape, you can understand the evolution of development processes. So our landscape becomes a seascape that moves over time. The ball is running down. And at the same time, things can happen. For example, a new attractor can come into place. And the system can be sort of sucked into this new attractor down here. So you have much more rich behavior. So the appearance or disappearance of new attractors is called a bifurcation event. And the bottom line is you don't need to sort of understand all the details of this, but the bottom line is that if you can reconstruct this sort of movie, this moving seascape landscape with its changing attractors and their bifurcations, then you have an understanding of what the process can do. Then you have reconstructed the shape, not only the shape of the developmental trajectory, but also the shape of the Waddington landscape that makes it be constrained that way. So that's the central point of this entire lecture. Of course, this sort of toy problem that I just introduced is hugely simplified. In fact, we have three maternal gradients. And in this case, four gap genes plus two terminal gap genes, Thales and Huckabind that we need to consider for pattern formation in the real system. So it's not as easy anymore to depict these landscapes in these high dimensional spaces, but we can still do the same type of modeling. But we need some mathematical tools. We can't just sit down and mentally rehearse the reverse engineering of the system. We need to measure the gene expression patterns quantitatively. And over time, we need to formulate a mathematical model that's depicted here. That looks very complicated, but it's quite simple. All it does, it's assuming that pattern formation is happening along only the anterior posterior axis here. So there's a row of nuclei that are arranged along this axis. They do divide, but that's all they do. So this is a great system because there's no tissue rearrangement, no growth. So all that's happening is that these nuclei divide every once in a while. And between each one of those nuclei, there are three processes that are happening. And these are described by a system, a very complex looking system of differential equations. A few things you need to know about these equations. This term here tells you that each equation describes the change in concentration of a gap gene product in a specific nucleus. So for each gap gene in each nucleus, there is one such equation. And the change of concentration for each of those gap genes depends on three processes, which are represented by different colors here. Let's start at the bottom because this is simple. Each gap protein is degraded at a very high rate. It's a very unstable system because the patterning is happening very fast. It's very important. The gradation rates are very important and often neglected by genetics. Think about this. This is another thing the model can give you. It redirects your attention to features of the system that you can study using genetics. One of them is the stability of the proteins involved. These proteins have to be degraded very quickly because, remember, the patterning here happens within one and a half hours, so the pattern changes on the order of just a few minutes. So these proteins cannot be more stable than sticking around for a few minutes. Another thing that's happening, because there are no cell membranes here, is you have diffusion of proteins between neighboring nucleus. That's in the yellow term here. And then all the interesting stuff is happening in the green term, which represents the mutual regulation of different gap genes and the regulatory influences of the maternal coordinate genes as well. So what you have here is two summation signs. And what that means is that there are different regulatory inputs coming in, and they are represented in the system by a matrix of parameters, basically each genetic interaction. Here is the network diagram. Each of the interactions, arrows for activation, T-bars for repression, each of those interactions is represented by one number here. If you take this number, it is sort of the regulation of target gene number one, in this row, by regulator number two, this column here. So if this number is positive, this interaction is an activation. If it's negative, it's a repression. And if this number is zero, or very close to zero, then there is no interaction. That's another possibility. So this matrix of interaction parameters describes the entire network structure or topology, all the different interactions between the two. This whole sum of regulatory interactions is then fed into a sigmoid activation expression function, regulation expression function. So basically, if you have zero is here, if you have positive input, the gene will tend to be on at its maximum rate. If you have negative input, the gene will tend to be off, and there's some sort of leakage involved. Very simple. Activation dominates, the gene is on, repression dominates, the gene is off. These sort of shape curves are called sigmoid curves. They make the model nonlinear. So the switches that are happening in the system make the model nonlinear and unpredictable. So what you do is you take sort of a random set of numbers here. So a random network, and you simulate it, and you check, what does it do? And you compare the pattern that it creates to the real pattern. And it will be terrible. Okay, so a system with random numbers will generate a random pattern. And what you can then do is you can use optimization algorithms that function just like evolution really does in nature. They're literally evolutionary algorithms very often. And they sort of change randomly the numbers in here and select better solutions over time. If you do this a couple of million times and you always go back, and you select solutions that fit the actual data a little better. Then at the end, you will get a model that reproduces this pattern. If you're lucky, you'll get a model that reproduces this pattern precisely. Okay. And this is what I did during my PhD. So we took these models to a big data set of gene expression data in Drosophila melanogaster. Based on immunofluorescence, you can see some example patterns over here. Remember that these are time series of data. And so if you represent this by a graph on the left here, you can see early expression patterns of the Gapchins. This is hunchback in yellow, croupling green, Knurps in red, giant in blue. And at the late blaster term stage, they look like this. And so you can draw the sort of trajectory in between because we have a lot of data points, which looks like this. So you have the peaks of the domains are represented by lines here. And you can see that the area of the domain is represented by the background color. So you can see that these domains, they shift over time to the interior and they become narrower. It's sort of like an accordion movement. So you squeeze the accordion towards the interior of the embryo. And they become sharper. The boundaries become sharper and more well defined. So you end up, you come from this pattern, you end up here. And you have posterior domain of hunchback comes up in the posterior. Fortunately for me, when I was a PhD student, the model fitted this pattern very precisely. Here you can see the model output early on and late and the intermediate sort of dynamics, which reproduces this very well. And one thing should strike you here. And that is this sort of accordion shaped movement of the domains. That is not in a French flag model. That is something new. So the domain shift happens in the system. The domains shift and move to the interior. So this was very interesting and we wanted to find an explanation for it, but there are no mutants that affect any of those shifts in particular. So you cannot use genetics to study that, to study the mechanism that drives this shift. You need to have a model. So this is an example of a phenomenon in development that cannot be explained by doing. Later on, and this will become important when we look at evolution. We showed that you can use much more primitive data in situ hybridizations, color, I mean, colorimetric only semi quantitative to fit the model and it works. So what's really important is to get the timing and the position of the boundaries of these domains, right? As long as you do that, the model will fit and will explain. The model will provide a consistent network mechanism for the system. And this is depicted here, a slightly unusual spatial representation of a gene network. What I'm doing here is I'm drawing sort of the area of the embryo anterior to the left, posterior to the right, and the background color of the square indicates the maternal gradient that's dominant in the interior. The bicoid and the posterior, it's called the boxes indicate where the gap domains are located. And you can see our old friends, giant and crouple here. We're not looking at the head region, which is further to the anterior. You can see giant and crouple here and how they repress each other. We've already been there. We've done that. There's a second couple like that hunchback and Knurbs mutually exclusive expression pattern and strong neutral repression between each other. These staggered domains of mutually expressing gap genes, this is the basic mechanism behind the spatial arrangement of the gap domains. Now, what's interesting is that there is an additional layer of repressive interactions that are much weaker. They occur between factors that are co-expressed in the same nucleus. Hunchback represses, giant represses, Knurbs represses, crouple and crouple represses, hunchback. These interactions have to be very weak because otherwise the two factors couldn't coexist in the same nucleus. But for this reason, geneticists have always debated about whether these interactions were real or not. In particular, the group of Mike Lewin would detect one of the interactions and the group of Herbert Yackel would deny that they exist. So endless amounts of discussion about this. It turns out in our model, these interactions are real. They're very weak and as you can see, they are asymmetric. They are going from the posterior to the anterior. And what they do, and the model shows you that, is that they cost is accordion like squeeze and shift of the women. So the geneticists, they were not sure about these interactions. Not only are they very weak, but they also didn't know why they were there. And now with the model, we can say they are there to cause the shift. You add a bit of oppression from terminal gap chains here in the terminal region and you get a complete sort of mechanism for gap chain expression. And so this illustrates how we first decompose the system into the factors and their interactions and now using the model. Recomposed it, put it together again, and we can now understand features of gap chain expression like those shifts that cannot be studied using genetic and molecular approaches alone. But this is not really it, right? Again, it's just a network picture. So how can I claim that I understand this, as opposed to Eric Davidson's big network where I said this is just a challenge. We don't understand what it does. The thing is that the model does something very important. It gives you the tools to look at what's happening at each time and space point and analyze which genetic interactions are contributing to which particular feature of expression. So if you do this, you will see that these sort of gap gap interactions are shifting the French flag. So a while back, I've introduced this idea of a drunken French flag that is no longer static. It has a time arrow going down here and you start, I didn't talk about this. You start from a fairly fuzzy and imprecise maternal gradient and you make boundaries that shift over time and become increasingly precise. Okay, which is another phenomenon that's sort of astounding and interesting to study. So in the end, you have a French flag pattern, but there is no more correspondence between any specific concentration thresholds and the gradient and the final position of the domains because those depend on gap gap cross regulatory interactions such as the ones we saw in the previous slide. Okay, so positional information is now dynamic. It no longer is a simple sort of readout of a gradient like suggested in the original French flag model. So how does this work? Okay, is this magic? What does the model help us in terms of understanding the mechanisms of this shift? And so what's really interesting here is two observations. First of all, in the interior of the embryo in this sort of blue, yellow and green area here, the domains don't shift. Okay, they look very similar to the posterior. In these sort of series of graphs, you can see in this red area here, if you squint a little bit, you can see that the domains just look at the Knurbs domain. It starts here and it shifts dramatically to the interior. While the boundaries here, they stay more or less at the same spot over time. So despite the gap domains looking very similar, it seems that very different things are going on. So how do you get this shift in the domains? What is happening? One thing that's very important to notice is that there is nothing moving through the embryo. This mechanism works if you switch the fusion off. So unlike Turing mechanisms, this is a mechanism that does not depend at all on diffusion. It is not the Turing style pattern system. It depends on the particular way in which these genes interact. And the secret to understanding this is to look at each nucleus in the posterior here individually. If you look at different nuclei here, and I'm representing each one of them as a column, you start early on with different concentrations of a maternal gradient from a hunchback gradient, and that triggers different trajectories. So in a nucleus here, you have Kruppel at the beginning and you just keep on expressing Kruppel till the end. As you go more posterior, the nuclei will switch from Kruppel early on to Knurps. Here, a little bit of Kruppel in the beginning still, but mainly Knurps. Then Knurps switching to Giant. More extreme even here as you go more posterior. So basically what you're seeing here is not a shift, but a sort of a coordinate succession of different gap genes that are being expressed. And you can depict this on a little collar wheel here and say, okay, each one of those nuclei is going through a different part of this collar wheel. And you can think of this collar wheel as a clock. So basically what you have here, and this is very surprising, is you have an oscillator. Okay, so these cells oscillate through the expression of a stereotypical succession of gap genes. They go from Kruppel, Knurps, to Giant, to Hunchback. They all end up with an attractor that only expresses Hunchback, but they never get there. They all just go through about a quarter of an hour of the clock and then they stop. So it's a really, really bad clock. And it's not an oscillation, even though it is driven by an oscillator, because the expression patterns never repeat. It's like a really, really shitty clock that only goes through about 15 minutes of the hour before it breaks down. But nonetheless, it's an oscillator that patterns the posterior of the embryo here. So to summarize this, in the interior, you have a completely different system where you have different attractors just like I showed you before between Giant and Kruppel. So different nuclei fall into different basins of attraction, and they converge to different attractors. So you have switch-like behavior. The nuclei switch between the expression of different gap genes depending on how much maternal gradients they experience. While in the posterior, you have this really bad oscillator mechanisms. And not even though the patterns overall look very similar, the mechanism is very different. We had a reviewer of this paper say, the difference are so subtle, they're not important. This is idiotic, okay? It is not the subtlety that makes something unimportant or important in biology. What I would say is we detected a really subtle but important phenomenon here. That proves that our methods of looking at were really good. Didn't convince reviewer to there very much. Because even though the patterning differences are subtle, okay, the shifts are subtle, they indicate that there's completely different types of interactions going on. So the system in the interior is like you start somewhere, and that determines where you end up. So just like this system here, depending on where you start, you end up in an attractor of a different color. While in the posterior, it is a damped oscillator, a very strongly damped oscillator. So strongly that it never really oscillates and repeats itself. Okay, and this system is much more alike to kids on a swing, if you don't push them, they will stop swinging. So qualitatively, very, very different patterning mechanisms underlying these very different subtle shifts in expression, timing and dynamics. We wanted to know as a next step, okay, this is nice. We have mechanisms in the sense of an oscillator, a switch, but what we want to know is which parts of the network are involved in what kind of behavior. And so what we did is we subdivided the network into three areas, depending on the region of the embryo. And what is striking is that, you know, there are four gap genes that are active in the system, but only three of them are expressed in the anterior, the center, and the posterior of the region we were looking at. So in the anterior, you have hunchback, giant and crouple. In the middle, you have hunchback, and crouple. And in the posterior of Knurbs, giant and crouple. Three different sets of genes, they all share two factors with each other, so hugely overlapping, but also interesting, look at the interactions between those genes. They're all the same. Okay, and they are like this. These interactions correspond to our old friend, the ACDC circuit that we looked at in the first lecture. Okay, so each one of those circuits is composed of different genes, but has exactly the same structure. How can that explain different behavior in the anterior versus the posterior of the embryo? Usually, we think of different behaviors as implemented by different networks. Here, and this is important, you have the same network implementing different behaviors. And what's important here is that because it's the same network with different genes, the strength of the interactions between those genes is different in the different regions of the embryo. And depending on those interactions, each one of those sub-circuits of the whole gap gene system, they call them ACDC1, ACDC2, and ACDC3 shows a different type of behavior. So this is all nice and good, but I'm an evolutionary developmental biologist. So what we wanted to find out is how does this system evolve? And for that reason, we looked at two different sort of very distantly related species to Drosophila melanogaster. One was the mothmage, clogmia, albipunctata, a very cute looking fly that lives in the sewers, mainly of Mediterranean cities when I lived in Barcelona. In Barcelona, we had a lot of them and they were an indicator of bad hygiene, especially in restaurants and bars where you shouldn't necessarily eat. The second species we had in the lab is called megasilia ptida scuttle fly, also called coffin fly, because it lives mainly underground. It doesn't fly very much and it eats dead bodies of animals. So it's very easy to keep in the lab because it eats anything that rocks and it doesn't fly away very easily. And these flies, here's a phylogenetic tree, if the flies in the mosquitoes, the dipter have sort of interesting positions in this tree. So up here on the left, you have Drosophila melanogaster and I've indicated the maternal coordinate gradients here and the gap gene domains that we were into before. So I'm summarizing what was known when we started this project. And these are different fly species and a mosquito here where people had done work on. So you can see two really big branches in the dipter. One is the branch of the mosquitoes that also sort of includes certain midges like clogmia out here. And then there's a group of flies called the cycloraphan flies. Unfortunately in English they're called the higher flies. I think mosquitoes would disagree with that. And they have radiated, diverged about 180 million years ago. And what's interesting here is only these flies in red here have big gradient which was thought or and is still thought by many people to be crucial for this pattern. Remember I said you only understand the principles of a system, what is accidental, what is really necessary if you compare it between different species. So what we're going to do is we're going to focus on a specific species here, megasilia, which is an early branching cycloraphan from an early branching cycloraphan lineage. And we're going to look at how it sets up its gap domains. Interestingly it doesn't have a maternal caudal gradient. So what is interesting to look at here is not how the gap gene domains change. They're pretty much the same in all those species, but how they do not change in light of very drastic changes between maternal gradients. This was work done by Eric, by Urs Schmidt Ott, I'm sorry, in these different species, previous to our project. And he was also the one who introduced us to megasilia. Cannot acknowledge it enough. Okay, so one thing we did is we just did 30 years of Drosophila genetics in a few months in megasilia. We took a massive amount of RNAi and my wonderful postdoc Carl Wharton knocked down all the different gap genes and all the maternal genes in megasilia. And the good thing about RNAi, which is usually a bad thing is that it creates this sort of series of effects. It has a sort of varying effects in different individuals, which means that we got a sort of a quantitative series of the strength of an effect in one experiment. So in our case, the sort of variable effect of RNAi was not a nuisance like it is in most cases, but it was an indicator of how strongly an interaction affected the network. So we reconstructed gene by gene, the effect on all the other genes, and created large quantitative data sets that documented the variability of gene expression in each one of those nuisance. At the same time, we used our reverse engineering approach. So we created quantitative data sets of gene expression in all these different species, and fitted our mathematical model to those species. So with that, we not only get a sort of a putative interaction network, but also always the sort of dynamical behavior to switch like versus oscillator behavior from the face portrait of the system. Okay, so after six years of work. To our great first initial disappointment, it turned out that Megazilia had exactly the same gap gene network, more or less as Drosophila, but not quite what we did find out through our RNA experiments and the predictions from the model is that the strength of the interactions vary between the two species. In particular, look at those interactions between overlapping gap genes, they're much stronger in Megazilia. So the models showed us that the behavior of the shifts was the main thing that differed between Drosophila and Megazilia. And this is depicted here again such time diagrams like I introduced before so you have early up here late time points down here and you see the boundaries of the domains move in different simulations in the background color indicates the position of the gap domain in the data. Now what happens in Megazilia compared to Drosophila is that the pattern start out much further posterior because there is no caudal gradients, the posterior patterning is delayed. And there's also a broader big wave gradient. So basically the whole gap gene pattern is sort of much further shifted to the posterior, and then nothing happens in the beginning look at giant here doesn't shift until a later stage and suddenly it starts to shift very strongly. And also, in the anterior, you have hunchback, which is shifting now and remember in Drosophila, this was a boundary that didn't shift so here's a delayed shift in the posterior and an increased shift in the interior of the embryo. So what evolution does, it seems to be modulating the shift behavior of these different gap genes in different animals and what we found out by analyzing the models is the following that these different ACDC circuits are present in all different species, but they do different things so remember in Drosophila in the anterior you get a multistable switch and stationary domains. In the middle, I didn't tell you that, but this circuit does both switching and oscillation so somewhere in the middle there is a bifurcation that occurs. So any sort of circuit that is close to a bifurcation is called critical, the behavior is critical, it could change, it's kind of labile to evolutionary change and this will become very important later on. And in the posterior we have a circuit that robustly produces the dammed oscillator behavior that produces the shape. Now in Megazilia, this is different so that the strength of the interactions remember between overlapping gap genes have changed and so the ACDC number one has now gone critical here and this is why we see domain shifts here while these two ACDC two and three produced dammed oscillations so we see much more widespread oscillations but they also have a different dynamic than in Drosophila. So it seems like the overall arrangement of the gap domains strongly conserved between different species across 180 million years of evolution, while the bifurcation boundary that leads to the change between static and shifting boundaries, its position has changed and is labile towards evolutionary change. This tells you a lot about the evolvability of the system that certain features random changes in the genes will create non-random changes at the expression level. And it also tells you that the shifts themselves, the boundary between a shifting regime and a switching regime are what are evolving in the system while the overall arrangement off the gap genes remain very similar. Okay, you can take this a little further and you can analyze the model and see if you can push these ACDC circuits into the domain of stable oscillations and if you're interested you can read up in this wonderful paper by my PhD, former PhD student and soon to be professor in Oxford Berta Verde, you can analyze the system and show that it can be pushed into stable oscillations which corresponds to a short term band type of development. So, what we've done here with the model is something completely different from what James Sharpe and his colleagues did in the fin-to-limb transition. What we've done here is we've looked at the genotype phenotype map and we found out that there's an entire level of complexity between the genotype up here and the phenotype down here, which consists of what I would call configuration space, it's a bit like the phase space, the state space and the different parameters, combined and in that abstract space, which Waddington called the epigenotype, in that abstract space there are different domains of shifting, switching behavior and the genotype phenotype map maps through this complex landscape for which Waddington's landscape is a metaphor, this sort of dynamic landscape that consists of the tractors and their bifurcations. So by studying these attractors and their bifurcations, remember we're reading those attractors and all those features of the process out of the data by reverse engineering the system from data. This is measured, this is reconstructed, this is not just theory, this is empirical research, these attractors are real just in the sense that the gap genes are real that constitute the system. Okay, so we've reconstructed this and this allowed us to study the evolvability of the system. Okay, which depends on the geometry of this configuration space. So focusing on the genotype only by just doing genetics, you will not find the principles that govern the system. A few more thoughts on this. Comparative analysis shows us that things that are crucial in Drosophila, the big weight grading, you know, and other things are not essential in other species. So they can be replaced, they're not essential design principles. Okay. Also, the shifts are labile, the basic arrangements of the domains are not. Okay, to summarize this stable boundaries in the interior of the embryo set by attractors switches moving boundaries in the posterior they're governed by a damth oscillator evolution adjusts repression strength to tweak the dynamics of stationary versus moving boundaries. And so you could think of these moving boundaries, almost as a living a dynamic fossil of the original short term band oscillatory way of making certain pitch. So we've used the model here that is very strongly based on data to get an insight into the evolution and the function of the system that we couldn't get after 30 years of Drosophila very careful Drosophila genetics. So the two approaches, correct, or complement each other, they're both used, best used together they're not in competition. Which brings me to sort of the final overall summary of the whole lecture and that is development is complicated to study developmental biology, you've already found out probably. So it's so complicated that we can't explain its mechanisms without relying on computer models that was the basic point in lecture one models also give us a different dynamic perspective on development that complements the genetic perspective in both cases of the developmental limb transition and of the flies. I showed you how reconstructing the dynamics of the process tells you a lot about the functioning of the pattern system but also the evolution of the pattern. They not only tell us how developmental mechanisms work, but also how they can change during evolution comparative analysis are necessary to understand the design principles of the system they allow you to to distinguish what is accidental and what is really an essential part of the working of the system. So, I suggest that we use a lot more sort of reverse engineering comparison. And if we do that, we finally get a truly mechanistic process based dynamic insight into how developmental processes work and how they will. Without modeling, you cannot do this. Thank you very much for listening questions comments you know where to reach me. And I hope you enjoyed this lecture. Bye now.