 Okay, good morning. Good morning. So I, just to remind you, we were talking about morphogenes and the control of spatial pattern in developing tissues yesterday. So I want to, and we sort of had this kind of structure, so we talked a bit about each of these things. So I want to briefly recap on these ideas, but do that by focusing on the neural tube, the system that I'm particularly interested in. And so to do that, just let me, first of all, just briefly introduce you to key aspects of the vertebrate neural tube. So as I assure you all know, the neural tube is the central nervous system of vertebrate embryos. We particularly focus on the spinal cord. And we do that because it's an important part of us, you know, it's one of the defining features of others, vertebrates. But it's also functionally important. So it allows us to perceive our environment by touch, pain, heat, et cetera. And also control our response to our environment by controlling motor output. It's part of the central nervous system and it's arranged in a very similar manner to the rest of central nervous system with functionally distinct neuronal subtypes being spatially segregated. So in the dorsal spinal cord, so that's a bit of your spinal cord closest to the skin of your back, are neurons which receive sensory information from the periphery. They process that information, either sending it up into the brain or down into the ventral region of the spinal cord where the interneurons and motor neurons that control motor output are located. So that arrangement with the functionally segregated positioning of those different neuronal subtypes arises early in development with the segregated generation of different neurons. So we go back in development from the adult spinal cord to the embryonic spinal cord. So this is actually a cross-section through a chick embryo about 48 hours after the egg was laid. So at this time you can already see an established dorsal ventral axis. But at this point in time most of the cells within the forming spinal cord are proliferating progenitors. They're highlighted here in red. So these occupy the most medial aspect of the neural tube and it's an epithelium with the apical surface on the inside and basal surfaces around the outside. So progenitors are located at the apical surface towards the apical side of the neural tube. But it's a pseudostratified epithelium with these nuclei, these cell bodies, undergoing apical and basal movement during this time. As progenitors commit and differentiate into post-mitotic neurons, they migrate in an apical to lateral direction. So first born neurons are situated around the lateral edges of the neural tube and here they're identified by the green staining. And already at this point in development there's dorsal ventral pattern. So along the dorsal ventral axis we can distinguish distinct neuronal subtypes based on molecular gene expression patterns, molecular profile. Similarly along the dorsal ventral axis of the progenitors we can also distinguish distinct domains, distinct blocks of progenitors. And we can do that with a set of looking at the expression of a set of markers. These are all transcription factors. So if we look at this set of transcription factors, what you notice immediately is that they are all expressed in progenitors but each of them has a slightly different domain of gene expression. So in these first four slides here, the first four images here, the green genes are expressed in the dorsal neural tube down to some ventral limit and each of these has a slightly different ventral limit of expression. And the two red genes here have the opposite characteristic expressed from ventral to particular dorsal limits of expression. So we look at the combination of genes expressed at any of those positions along the dv axis, we can uniquely identify that position. So the combination of gene expression allows us to define domains of progenitors arrayed along that axis. Work I'm really not going to get into today indicates that this combinatorial transcriptional code is responsible for neuronal subtype identity. So if we manipulate this code, so knocking out genes or mis-expressing genes, then we have predictable consequences on the neuronal subtype generated. So if we want to understand how you generate that spatial pattern neurons, what we have to do is to understand how you generate this spatial pattern of gene expression within progenitors. And as I mentioned yesterday, this pattern of gene expression is dependent on signals emanating from the dorsal and ventral poles of the neural tube. And today I'm going to focus on the ventral half of the neural tube and hedgehog signaling. So sonic hedgehog secretic glycoprotein, which is produced by notochord, a rod of axiomies dermal cells that underlies the neural tube, and slightly later by specialized cells at the ventral midline of the neural tube itself called the floor plate. Okay, so just before I get into sort of the developmental biology details, I just want to re-emphasize this. There is a functional consequence here. So you want to generate the right types of neurons at the right position because that's essential for establishing functional circuitry within the neural tube. So to make the complicated feedback circuits that allow us to coordinate and control motor movements, then you need a highly complex circuitry within the spinal cord. And that first step in generating that circuitry is making the right number of neurons the right type in the right position. But now I've said that I'm going to completely ignore this and we can just sort of focus on the abstract problem of how you generate these patterns of gene expression. So there's several lines of evidence that hedgehog signaling is important for generating this pattern in the ventral neural tube. And several lines of evidence that some type of graded activity of hedgehog is important. So for example, we can recapitulate this in vitro with different concentrations of recombinant hedgehog. So we take an early chick embryo. So this is a diagram of a tensomite embryo. And we can explant out a little region of the forming neural plate. So cells which will go on to become the neural tube. And we can culture that ex vivo in tissue culture. And now I've defined concentrations of recombinant hedgehog to those cultures. So we just take one of those ex plants, culture it without any added hedgehog, and then we look at gene expression. Then the majority of cells in the absence of hedgehog express gene expression such as PAC-7, characteristic of the dorsal neural tube. If we add a moderate concentration of hedgehog, so this is one nanomolar hedgehog, then PAC-7 is no longer expressed. And instead we see this red gene, Olig-2, which is characteristic of the middle of the ventral neural tube. So in fact, Olig-2 is expressed in those progenitors, which will go on to generate motor neurons. So these are your future motor neurons. If instead of one nanomolar hedgehog, we use four nanomolar hedgehog, then instead of the red gene we get the green gene, and the green gene is another transcription factor, Nkix-2-2 expressed in progenitors, ventral to the Olig-2 domain, right adjacent to the floor plate, the source of hedgehog itself. So this is sort of classic kind of data, which is interpreted within the context of that morphogen idea. So different concentrations of hedgehog result in the induction of different gene expression, and the gene expression induced, the concentration corresponds to the position within the gradient one would expect to see those cell types. But of course it's more complicated than this. So these explants are all assayed 24 hours after we've added hedgehog to them. But we can look at similar explants at different stages after the addition of hedgehog. So here we're using that high concentration of hedgehog for nanomolar, which at 24 hours induces a high response gene Nkix-2-2. But if we look at explants treated for 12 hours with high concentrations of hedgehog, now many of the cells in those explants express the red gene, the low response Olig-2 gene. And we can see a transition from Olig-2 to Nkix-2-2 over this time period. So if we count the number of cells expressing each of the responding genes, we see Olig-2 being more rapidly but transiently induced by high levels, high concentrations of hedgehog, whereas Nkix-2-2 is delayed in its induction, and its induction correlates with when Olig-2, the number of Olig-2 expressing cells is decreasing. So somehow we need to explain why we're getting these dynamics in gene expression. I'm going to, yeah, I mean, the next half an hour hopefully I will explain that. And then, which is related to this point, we need to think about, so this is looking at the extracellular concentration, manipulating the extracellular concentration of hedgehog. But as you remember yesterday, we discussed this idea that signal transduction pathways introduce dynamics and there might not be a straightforward relationship between the extracellular concentration of hedgehog and intracellular signaling. And indeed, remember, so in the case of hedgehog signaling, the GLE proteins are the transcriptional effectors of hedgehog signaling. And if we measure GLE activity within the neural tube, then we see complicated dynamics of GLE activity. So just to remind you of this plot, this is looking at developmental time along the x-axis, then GFP intensity, which is monitoring GLE activity. And each of these lines represents different positions in the neural tube from ventral, 0% of the ventral midlife up to 50% in the middle of the neural tube. So if we look at any one particular time point here, we see high levels of GLE activity ventrally decreasing as you move dorsally in the neural tube. But if you look over time, then the amplitude of that gradient changes quite markedly. So if you think about a cell, if you think yourself into a position of a cell sitting somewhere within the ventral neural tube, then you're seeing, you're harboring different levels of GLE activity over developmental time. And somehow you're using that dynamics of GLE activity to generate those spatial temporal patterns of gene expression. So the challenge is how do we accommodate, how do we account for these observations? So what I want to argue is that this spatial pattern of gene expression in response to those complicated dynamics of hedgehog signaling are dependent on the downstream response of cells. So as well as being nice markers for different progenitors in the neural tube, these are all transcription factors and they're linked together by regulatory interactions. So specific regulatory interactions between these genes generates a transcriptional network. And I'm going to argue it's that transcriptional network which is essential for converting the dynamics of GLE activity into these temporal spatial patterns of gene expression. So some of the evidence for this comes from straightforward developmental genetics. We can knock out one or more of these genes and ask what happens to the remaining genes. So I'm going to illustrate this by focusing on this boundary here. Damn it, I keep meaning to change the cycle because the colours are mixed. So if we focus on this dorsal boundary of Nx2-2, so you can see that this corresponds to the ventral limit of Pac-6 which is expressed throughout dorsal progenitors with the exception of the Nx2-2 domain. In addition, Olig-2 is also... its ventral limit expression is also corresponding to the dorsal limit of Nx2-2. So these progenitors here express a combination of Pac-6 and Olig-2. We just said they're coming by different distance. You don't have to cite an Olig-2. Right, so at this point in development, so this is the first wave of differentiation. It's entirely neurogenic. So in fact, and this I'm not going to talk about this at all, the switch to gliogenic generation happens at a later time. So in mouse, I'm talking about the period of neural development from about E8.5 to E12.5. Subsequent to E12.5, there's a switch to gliogenic generation. However, all of these cell types will be generated prior to E12.5 and they're not generated subsequently. So in chick, this corresponds to... that this transition to gliogenesis happens at about embryonic day 4 to 5. In humans, this would be... so this period of neurogenesis in humans would be at about the four weeks after fertilization and the gliogenic switch happens a week or 10 days later. So this is purely neurogenic. You don't generate glios cells at this time point. So if we just focus on this boundary here, then we can look at the effect on NKX22 expression when we knock out Olig-2, Pax-6, or both Olig-2 and Pax-6. So that's the image you just seen in wild-type embryos. So if we knock out Olig-2, there's no Olig-2 protein and what you notice is a small but noticeable expansion in the dorsal limit of NKX22. In a Pax-6 mutant, remember Pax-6 is expressed throughout this region. In a Pax-6 mutant, there's a more striking expansion of NKX22 and concomitantly some repression of Olig-2. And notice that cells remain green and red, right? So there's still a mutual exclusive expression of Olig-2 and NKX22. But there's more NKX22 cells. In a double mutant lacking both Olig-2 and Pax-6, now that expansion of NKX22 is really quite marked. And you can see, so just by eyeballing this, this new domain of NKX22 appears to fill both what would normally be the NKX22 and Olig-2 domain in wild-type embryos. And indeed that's the case. So if you measure the position of this new dorsal limit of NKX22, it corresponds to where you would normally expect to see Olig-2 being expressed. So if we think about this from just interpreting the genetics, then what this is suggesting is that the differential response of NKX22 and Olig-2 to hedgehog signaling is actually dependent on Olig-2 and Pax-6. If we remove Olig-2 and Pax-6, now NKX22 responds very similarly to Olig-2. So that suggests that this downstream transcription network plays a major role in interpreting a graded hedgehog signaling. So we were interested in trying to address that question in more detail. So to do that I'm going to introduce one further transcription factor. So the fourth one I'm going to introduce is a transcription factor called Iroquois-3, also expressed in neural progenitors. And like Pax-6 is expressed throughout the dorsal neural tube, and its ventral limit of expression corresponds to the dorsal limit of Olig-2. So these four transcription factors define two boundaries at different positions along the dorsal ventral axis. So the Olig-2 Iroquois-3 boundary and this boundary we just looked at between the dorsal limit of NKX22 and the ventral limit of Olig-2 and Pax-6. So the type of genetic experiments and both loss of functions, which I've shown you in gain of function experiments, suggest a set of regulatory interactions illustrated in this cartoon with cross oppressive interactions noticeable, really dominating the interactions between those four transcription factors. In addition, as I've shown you a few slides ago, both Olig-2 and NKX22 depend on hedgehog signaling for their expression. So you can absolutely get similar results. So one way we've done that is using, and the way we do that these days is not using explants but using ES cells which we've differentiated to neural progenitors and then adding appropriate amounts of hedgehog or hedgehog agonists to that. So no, we don't have any evidence that cell-cell interactions are important. In addition to those type of experiments, the type of experiments I showed early on yesterday where we were ectopically expressing patched in small groups of cells in the intact neural tube and seeing cell-autonomous changes in gene expression also argue against any major role for cell-cell communication. So in those kind of manipulations, you're also seeing a cell-autonomous effect. Adjacent cells are behaving as they would do normally. So I'm going to come on, hopefully, come on to biochemistry later on. Yes, and that's going to become important in a few slides time. So in amniotes, so chicken, mouse, where we've looked at this, again we don't find any strong evidence for cell arrangements. So it's a sort of stratified epithelium. So when we look at clones, so marking individual cells looking at the shape of clones later on, so sisters stay relatively close to each other, they don't disperse very broadly, and there's no evidence that clones at the boundary have a different shape to clones within the center of a domain. So that's sort of negative evidence, but it's consistent with an absence of any effect on cell rearrangement or the cell adhesion. But I think it's still an open question and still needs more attention. Okay, so we've got a genetic network here. So the questions we wanted to ask is, so can this network explain the spatial temporal behavior in gene expression? And if so, how is it doing that? So the way we approach this is to convert this cartoon into a dynamical systems model so we can take those interactions and then describe them by four linked differential equations, so we're using a particular formulation to describe gene expression based on a statistical thermodynamic description of gene regulation. The details don't matter so much, but what we're describing is that each of the components, each of the transcription factors within this network are regulated as described within this network and then have linear degradation. So in terms of the regulation, then there are sort of, there are three components that can go into that regulation. And the reasons for this will come back to shortly. So the three components are for NKEX22 and OLIC2. They have a hedgehog signaling input. And remember that glee activity in the absence of hedgehog is a repressor in the presence of hedgehog is an activator. So NKEX22 and OLIC2 have an input from hedgehog signaling. All four transcription factors have inputs from a spatially uniform basal activation and that will become important. And then the third input is the network input, if you like, the repressive interactions as described by this cartoon. So we're taking this cartoon, turning it into four linked differential equations. And then obviously we need to parameterize this. So to parameterize this set of equations, we've taken an optimization approach. And to do this, we've collaborated with Chris Barnes at University College London who has been developing an optimization approach along with other people based on approximate Bayesian computation. So I think most of you will be familiar with optimization strategies. This optimization strategy, like many others, the basic principle is that you start off with a parameter space. So in our case, we have, I think it's 14 or 15 parameters in our model. But just for illustrative purposes, if you imagine a model with two parameters, you pick specific values for those two parameters from initial range, possible range of parameters. You simulate your model with that choice of values and you end up with some output of your model. You compare that output to some target objective and if it meets, if it's close enough to that target objective, you keep that parameter set. If not, you throw that parameter set away and you do that several billion times. There's also some other computational magic in there as well. But what you end up with is a set of parameter values which meet the criteria you've set out to do, you've set out to accomplish. So using this particular approach, one of the nice features of using ABC is that you don't end up with just single parameter set optimized for your target. What you end up with is a set of posterior ranges, so the range of values which meet your target. So in our case, the optimization, the targets we wanted to optimize were the behavior of the model under the genetic perturbations that we knew from the experimental data. So we wanted the model to fit both the wild type spatial pattern but also the spatial patterns obtained when we knock out one or more of the components of the network. So you see at the top line here is these are the objectives set by the optimization and here is an example solution showing that this particular example solution meets fairly well the targets within that we set for the optimization. Yeah, yeah, and there's a lot of, yeah, exactly. So what we did in this case, we started starting, and I think that's an important point about optimization. There's a lot of often hidden features of optimization that you don't appreciate until you really go into the details. So one of those is initial conditions. So the initial conditions we chose were to what we felt represented the initial conditions in the neural tube which were to have high levels of Iroquo3 impact 6. So that's the expression of genes you would expect in the absence of hedgehog signaling, so equivalent of the dorsal neural tube. The other sort of, I mean, so doing more optimizations, one thing I've noticed is that the key thing with these optimizations is actually how you define your scores. How are you actually determining how good your outputs are compared to your objectives? Yeah. Right, and so one of the nice things about ABC is you get out these posterior distributions of possible parameters. So this is the output of that particular optimization. So these are all of the parameters which were unconstructed, which we were optimizing for. So exactly. So if you just look at these ranges, so what you can immediately see is that some of the parameters can have pretty much any value. So for example, this parameter here, which is actually the, so it's the strength of Iroquo3 repression on the NKX22. So that can take on pretty much any value, so it's unconstrained. It's not an important component to the model. Whereas other parameter values are much more restricted in the possible values they can take. And in addition, you can begin to see this, some relationships between certain pairs of parameters. And actually here you're seeing the marginal distributions of each of those parameters. But in this framework, we can also look at the joint distributions of parameters. So you begin to get a sense of the shape of this, whatever it is, 14 or 15 dimensional space. So if you look at these two parameters, so this is the strength of Iroquo3 repression on Olic2, and that's the opposite, Olic2 on Iroquo3. So you can immediately see that there's a difference there. So Olic2 appears to be a stronger repression, repressor of Iroquo3 than Iroquo3 is of Olic2. So this gives us now a parameter set which will perform the task we set it to. So it will give us those spatial patterns of gene expression. So one thing now with these posterior distributions is we can choose particular values for each of those parameters and go back and resimulate the model just to begin to look at the behavior. Any... Yeah, so that's some of the computational magic going on there. So I'd refer to Chris Barnes's work papers on the ABC technique. So it's not just simply randomly picking parameters and then doing that without any thought about what you're doing. But there are many optimization techniques, not only ABC. Okay, so if we do that, so now we take a specific set of parameters and we simulate the model. So now we're simulating this across a simulated ventral to dorsal gradient. So high levels of hedgehog signaling ventrally, decreasing as you go dorsal in the neural tube and looking at the steady state pattern. So consistent with the objective we set, we can see high levels of NKX-22 in a ventral stripe, Olig-2 in an intermediate stripe, and then high levels of PAC-6 in the request rate in the dorsal, at low levels of hedgehog input. So that's what we asked it to do and it's doing it, which is good. In addition, we can look in silicone at the effect of mutant, so we can look at a PAC-6 mutant. So this is just removing PAC-6 equation and what you can see is that you see an expansion of NKX-22 reduction in the stripe of Olig-2, no PAC-6, obviously. And so again, that's what we asked it to do and we asked it to do that because that's what the genetics were telling us. So this is all consistent with the objectives we set that the optimization appears to have worked. So what was more striking is when we looked at the behavior, aspects of the behavior we hadn't put into the optimization. So most importantly, we looked at the dynamics of the simulation. So all of the optimization was focused on the steady state behavior. But what we noticed is that the parameter sets that passed the optimization gave us back the appropriate dynamics. So if we simulate the model over time with a level of hedgehog signaling that a long time gives us NKX-22, we always see a transient expression of Olig-2. And remember, that's what we're seeing from the experimental data. So Olig-2 is transiently induced prior to the induction of NKX-22. So this is because we're looking at steady states here. So if you look at the simulation, you'll see, so at the dynamics, you'll see you're getting an increase in NKX-22 as Olig-2 is decreasing. So one simplification, of course, in the model is that we have a single equation for gene expression. In reality, of course, that's going to be a combination of RNA transcription and protein translation. But we're not separating that out in the mathematical model. So here, I mean, this is something we're interested in looking at in more detail now, here it would be interesting to try and disentangle that. So how much does the protein behavior lag behind the transcriptional behavior? They're all important, right? So here, if we've removed PAC-6, you also see a different behavior. So that's the full network. We manipulate, we remove PAC-6 and you get a different behavior. So it's the entire system. You can't, I don't think you can begin to say this component is important than the other's arms. Yeah, so in the model, we've non-dimensionalized time. So then we can just reimpose it when we do the simulations. So, and that's another interesting point. So what is it, what's controlling the time scale within the model? And the most influential parameters full of time scale are degradation rates, which you might suspect anyway. But so within the model, we can manipulate this time scale, these dynamics, by changing the degradation rate of the proteins. So in this particular, in these simulations we've got a constant gradient where it's temporally constant, but spatially non-uniform. No, and I'll come on to it. So as I showed you, in the real case you're seeing dynamics of signaling going up and going down. I'm just about to talk about that. What does it mean? I'm not sure what answer you want for that. So it's an observation so we're seeing, so there's a transient within the network in which you see a transient induction of Oligotube prior to the induction of Nx22. And experimentally we also see a similar transient expression of Oligotube prior to the induction of Nx22. I'm not quite sure what you're asking. Yeah, because we're not, in that paper we weren't considering this boundary. So effectively the simulation stopped there. Yes, so in fact if we have time I'm going to come on to describe analytical results which explain why you get that transient if we have time. So if we put these together, so we've got this, so in response to a steady state in response to a gradient, the spatial gradient of glial activity, we see these stripes of gene expression and dynamically we're also seeing this sequential induction. So there's, we can't, they're both a consequence of the same regulatory interaction. So we can't separate out that spatial and temporal behavior. They're both a consequence of the interactions within that regulatory network. So one way of thinking about this then is to sort of these, kind of draw this, what you might call a phase portrait of the system where we're looking at behavior over time compared to threshold, compared to, sorry, level of glial activity. So, and then the initial conditions as you see at time zero we're considering the initial conditions to be aero cross three impact six on so dorsal light condition. So what you can see if you look at this behavior then you see that to get the high response gene nkx22 you need a certain threshold, a certain level of hedgehog signaling higher than for the low response gene. But having that level of signaling isn't sufficient, you have to have it for long enough. So you need that signal for longer to get nkx22 than to get Olig2. And the only way to get from your initial state into an nkx22 state is transient through the expression of Olig2. So there's no way of getting into an nkx22 state without transiently expressing Olig2. So one thing this does then is to it connects the sort of gradient, the classic morphogen spatial and temporal behavior. And I just want to emphasize that point by just going back to mentioning this result from John Paul Vincent and colleagues looking at the expression of wingless in the Drosophila wing disc and reminding you their results indicating that wingless didn't need to be secreted to generate a spatial pattern of gene expression. But over time it's the pattern of wingless expressing itself changed. Suggesting that cells at the furthest distance from the later dorsal ventral boundary saw wingless for only a short period of time where cells close to the dorsal ventral boundary saw wingless for a long period of time. So in the context of this kind of dynamical system then either duration or level of signaling and actually a combination of both will give you the same result. So from the perspective of the nucleus from the perspective of pattern of gene expression it doesn't matter whether it's level or duration it's a combination of both which are necessary to create that spatial pattern of gene expression. The other thing that this begins to suggest an answer to is how cells are interpreting those changing dynamics of signaling over time. So again this system will so for example you can see how cells exposed to different levels of signaling over time will behave. So a transient high level of signaling if it's not sustained for long enough will not be sufficient to induce NKX2 too. So that observation suggested an answer to what had been an anomalous result within the field. I'm going to show you this it gets a little complicated but I think it's a good example of how this the mathematical model helped us understand some previous results. So this previous result is looking at a mouse mutant for GLE3. So as I mentioned there are three GLE proteins within vertebrates and GLE3 happens to be the main contributor to repressive activity. So in a GLE3 mutant if we compare wild type embryos to a GLE3 mutant at a level of GLE activity within the neural tube using that reporter for a hedgehog sign for GLE activity we see in a GLE3 mutant significantly increased levels of GLE activity consistent with GLE3 predominantly providing repressor activity. However surprisingly that increased level of GLE activity has little if any effect on patterning within the neural tube. So you see the domain of N-Kicks-2-2 in a GLE3 mutant looks similar to a wild type embryo. So that seems to be that seems to contradict this idea of hedgehog sign GLE activity functioning as a morphogen. However if we look more carefully at this increased level of GLE activity you can see that it's through early developmental time points but in fact it rapidly decreases back to normal level. So you see a transient increase in GLE activity which isn't sustained and it returns back to normal levels over time. So what could explain the transients in that increased GLE activity? So as I mentioned one of the target genes for hedgehog signaling within responding cells is a negative regulator patched. And so if we look at patched expression comparing control embryos to GLE3 mutants we see substantially increased levels of patched expression when we remove GLE3. So first of all that's consistent with that transient increase in GLE activity we're seeing more expression of the target gene in addition because it's a negative regulator of the pathway that would provide a way of regulating the level of hedgehog signaling and returning it back to more normal levels. And indeed that increased level of patched is present at early developmental time points but later on we see much more normal levels of patch within the neural tube. So put that together so we've got this transient increase in hedgehog signaling that doesn't lead to a change in the pattern in the ventral neural tube and I'm arguing that there's no change in the pattern because the effect of the transcriptional network buffers so you have a delay before you can induce NKX2 too. So the prediction then is if we perturb the transcriptional network at the same time as we increase hedgehog signaling then we should reveal a defect in the GLE3 mutant and indeed that's the case so again I'm afraid the genetics are complicated again here. So if we just focus on the NKX22 domain in the absence of GLE3 it looks very similar to a wild type embryo. In a PAC6 mutant I've already shown you that NKX22 is expanded in a PAC6 mutant. However if we look in a PAC6 GLE3 double mutant now that expansion of NKX22 is even more prominent so it's going up to about halfway in the neural tube. So the absence of GLE3 in a PAC6 mutant exacerbates the PAC6 phenotype even though in a wild type the absence of GLE3 has no effect. So that's consistent with this idea that the transcriptional network is buffering, is affecting the dynamics of how cells are responding to a hedgehog. Okay. So another feature of the that came out, another thing that the analyzing the model highlighted to us is this feature of bistability or hysteresis. And again if you're used to thinking about these type of models it won't be surprising to you given the amount of cross oppressive interactions within the network but it generates bistability. But this we thought could be particularly informative if we just think about the regulation of NKX22. So I've shown you that NKX22 requires the highest level of signaling to be induced. And that's because there's a regulation where all of the represses of NKX22 are expressed. Therefore to get NKX22 on you require sufficient level of signaling to overcome all of its represses. So once you've established NKX22 expression you've repressed its represses and now NKX22 is contributing to repressing its represses. And therefore you're able to sustain NKX22 with lower levels of hedgehog signaling. So you have to drop the level of hedgehog signaling significantly beyond the level required to activate it in order to return back to basal level. Sorry? I'm not sure I understand the question. So this is the level of NKX22. So there's an unstable state. There would be an unstable steady state between the two. Yeah, I haven't plotted it. So it's there. So this is a cartoon. This is not the full. Yeah. What happens when you simulate the model? Does it really work close to the steady state? I guess what I'm asking is it seems to be not a single link, right? Yeah, so one second for that. So that comes back to your question you had yesterday. Yeah. Yes, why one would have so we know from the genetics taking out PAC-6 has an effect. So that's what we're trying. So the bias stability, so again this will depend on the parameterization of course. So there will be some bias stability depending on the parameterization just coming from the other cross repressive the other toggle switches within that network. But the region of bias stability is sensitive to the various parameters describing those interactions. This is a one parameter bifurcation. I mean we haven't got a bifurcation diagram specifically here. I mean we can talk about I don't want to get into this really today but in fact this model will give you regions of tristability as well if you want. So again if we look at the whole bifurcation diagram we can find regions of bias stability and tristability. Okay, so this is right. So the prediction here is that you should be able to sustain NKX2 expression with lower levels of signaling than required to induce expression. So again that suggests an experiment. Again the experiment is a little complicated but it allows us to exploit the explants again. So the experiment here is we can explant those regions of neural tissue from chick embryos and then expose those explants to different amounts of hedgehog for different periods of time. So we just take one of those explants, expose it to high concentrations for nanomolar hedgehog for 18 hours we turn on NKX22. If you continue at that level of hedgehog signaling for 36 hours you maintain NKX22. If at 18 hours we reduce the level of hedgehog signaling and we're doing that by adding an inhibitor of smoothen and inhibitor of the hedgehog signaling pathway and we're reducing the level about three fold at the 18 hour time point then look at 36 hours we're still able to maintain NKX22 expression. If however we use that level of hedgehog signaling from time zero and assay at 36 hours we see that level of hedgehog signaling which is able to maintain NKX22 isn't able to efficiently induce NKX22 in those explants. So that's consistent with this idea of by stability. We can maintain NKX22 with a lower level of signaling that is required to initially induce it. So then okay so I've argued that this the network can also explain how the cells are interpreting these changing dynamics of clear activity. But there's also another feature of this which comes back to Stefano's question about so you can ask maybe why have these complicated dynamics of signaling. So another feature of these type of systems by stability is that close to these critical points are regions of where the system will change very slowly so you have this sort of what are often termed dynamical ghosts or dynamical slowing where essentially there's a ghost of the steady state left within the system so although it's not a steady state the system will change extremely slowly if you're within this region of parameter within this region of parameter space. So okay so just to illustrate this idea we can simulate the model with a level of activity that goes through the dynamical so we can use a level of hedgehog signaling that is far away from the bifurcation point. Sorry. The heterozygous we haven't documented a phenotype in the heterozygous so we've not noticed one but remember there's quite a lot of redundancy there so Onyc2, Pax6 and Iroquo3 are all able to repress Pax22. So okay so what does simulation look like so if we use a value of the activity that either goes through the ghost or is much higher and avoids the ghost so now we're looking in three dimensions here with Pax6, Olig2 and NX22. So the simulation start out at Pax6 you add activity to those and they transient towards an Olig2 state they don't end up in an Olig2 state instead the transient Olig2 then results in a system relaxing into an NX22 state. So if you look at the dynamics of this going near the Olig2 study state so through the dynamical ghost or avoiding that entirely what you can see is that if you're near that tension point then the cells the system really slows down through there you can see it really trying to squeeze through that region of dynamical space before eventually falling into the NX22. So that would suggest right so one possibility why you have these adapting dynamics is that gives you a way of avoiding these kind of regions of dynamical space so by having a high level of hedgehog signaling that then reduces it allows you to avoid going near the Olig2 study state but that by stability within the system allows you to maintain NX22 once you're in that study state. Does that answer your question? Okay so let me summarize what I've said so far. There's an argument that this transcriptional network, this circuit is sufficient to or explains how you generate two boundaries within the neural tube. It allows both the spatial and temporal concentration and duration of hedgehog signaling to be interpreted to generate these two boundaries and it has some other interesting features so it has by stability which could explain how you maintain levels of gene expression how you maintain these domains of gene expression once you've established them and the requirement for sustained high levels of hedgehog signaling suggests that it gives you some robustness to transient fluctuations in signal to get into the NX22 state you need to maintain high enough levels for a sufficient period of time. Yeah. If they're looking at your data do they look really sharp development but I'm wondering do you really think that noise is not in the system or in the process? Yeah and there's several sources of noise so I think you're thinking of signal noise which I think in hedgehog signaling activity which I agree there could be noise in that of course there can be noise stochastic noise actually within the system itself and this is a question we're interested in and we're trying to start to do some measurements to allow us to get some ballpark estimate of this. So I think there's possibility of noise in the signal possibility of noise within the circuit itself but in addition remember that this tissue is growing at the same time as the pattern is being established so an additional component of this is actually cell growth and the allocation of daughter cells within the tissue itself and that could also be that may actually be the most significant component for boundary precision and I agree the boundaries are reasonably sharp but they're not perfect so you do see misplaced cells and the boundaries are not straight with a certain wiggliness The mechanism you suggested trying to not to go critical fine maybe actually be more relevant to avoid that you have a lot of noise when you turn the cell on then you give a very different time of commitment if you had to put that part of the noise it's probably even more important when you're slowing down yeah yeah exactly that is true but I took the slide out so exactly so you can okay yeah yeah so these yes that's right so what is so maybe you can say that's exactly and all of this is happening much more quickly than what you've plotted on the x-axis of your axis of time no happening more quickly what do you mean happening more quickly because if it's a phase diagram then every point should be at the stationary point I see what you're saying yeah so this is it's a cartoon right and this is this is trying to illustrate that it is changing over time and it's also complicated because of the bistability right so this is not you know the whole thing is not a conservative system so in fact you've got to imagine that this is a snapshot of the phase portrait which will it will change over time depending on the position of the system within the landscape is that okay so for example the bistability will mean that crossing this boundary will change the position of this boundary how are we doing in time so I think so I'm gonna switch gears now so so 20 minutes so what I want to do now is in the last 20 minutes hopefully talk a little bit about the molecular implementation so I guess the genomic implementation of this circuit so I could do that or I could the alternative would be to talk for 10 minutes on more of the maths on an analytical maybe let's try this so less maths and more bioinformatics is that okay right so I've talked to you about the neural tube first of all I want to make the point about the gap gene system so you've already heard about the gap gene system being patterned by gradients of bicoid and caudal and the gap genes themselves like those neural progenitor transcription factors cross repress each other and if you look at the overall strategy of the gap gene system and many people have done this Thomas you heard about from earlier this week but many other people so Steve Small, Yogi Yaga John Reinet have also looked at the gap gene system and many of these things that I've told you about the neural tube also appear to be true in the gap gene system so graded signal regulating cross repressive transcription factors the combination of which generates dynamic spatial pattern within the tissue so how does this work at a gene regulation level so we briefly mentioned yesterday a little bit about enhancers and the fact that the enhancers are complicated so what I want to do is first of all summarize sort of an overview of what's known for a specific example in the gap gene system and then talk about some of our recent work trying to do a similar thing in the neural tube, us and other people as well so if we think about the gap gene system then if we think about a particular stripe of gene expression so an enhancer which gives us a regulatory element which drives gene expression along at a particular AP position that enhancer is active in that stripe of gene expression the work of again many people here is just summarizing this is a review I wrote with Steve which summarizes some of this so that enhancer will have several inputs into it so an input from bicoid which is your your spatial polarized input if you like so an input from the morphogen itself also inputs from spatially uniform express transcription factors so Steve and others in Drosophila have done a lot of work with Zelda which is an activator of genes expressed along the entire AP axis and finally inputs from the gap genes themselves so that repressive interaction so this is sort of the molecular equivalent to the components of that of the mathematical model so a morphogen input and then repressive input from the network itself and so in many cases those three classes of input appear to be integrated actually at the level of the cis regulatory elements at the level of the enhancers so you can find in enhancers in many cases which recapitulate these patterns of gene expression and looking at the transcription factors that bind to those enhancers they will contain binding sites for those three types of input for the morphogen the spatially uniform inputs and the network inputs the gap gene inputs and then the kind of transgenic enhancer bashing experiments can be done to ask what is the role for each of those inputs so while as an intact cis regulatory element recapitulates the full pattern of expression if you knock out individual components so the so this component here no longer able to bind then you see repression and vice versa so in each case you can look at the individual roles of those components and come to the conclusion that regulatory elements are integrating these three types of input so the repressive input from the network, uniform activators and then the morphogen effector so then if we think about this in the context of the network itself you can imagine the scenario where regulatory elements are essentially the edges in the network so they provide the means to integrate those three types of inputs and the dynamics created by the cross regulation to generate the dynamics we're seeing in the spatial patterns of expression so trying to summarize that then so how do at the level of regulatory elements how does the interpretation work how do you convert the graded input into discrete responses so it's the network itself which transforms the signal to pattern and the enhancers are doing that heavy lifting so they're integrating those multiple inputs uniform spatial uniform input and the network itself and that collective that network generates the dynamics we're seeing okay so this is increasingly well established in the gap gene system this kind of modular arrangement where enhancer elements are integrating these multiple inputs so it's the same principle at work in the neural tube so I want to summarize some data from my lab but also from other people's lab and I think the next two slides are going to be quite heavy so bear with me but I want to summarize at the end so first off so Tony Eustaveen working in Johan Ericsson's lab looked at try to identify regulatory elements associated with some of our favorite genes so some of which you've already heard about like NKX22 and Olig2 and so they've managed to identify regulatory elements which if they take those regulatory elements and use them to make transgenic reporters recapitulate many of the patterns of gene expression we're aware of so for example this element coming from close to the NKX22 locus drives in a pattern of expression corresponding to where the endogenous NKX22 gene is expressed and if you look at the transcription factor binding motifs within those elements you see evidence for glee binding so the morphogen effector you see socks binding sites so socks is a transcription factor which is uniformly expressed in the neural chi so it is equivalent to zelda and then in addition binding sites for what I'm calling the neural genitor transcription factors so the other components of the network so Andy McMahons lab Kevin Peterson and others in Andy McMahons lab went one step further and looked for biochemical evidence for binding of individual transcription factors and consistent with the bioinformatic analysis then they can find evidence that glee proteins and the socks proteins are biochemically binding to many of those elements so we've got so far two components of this idea so morphogen effectors and uniform activators binding to the regulatory elements binding to the same regulatory elements associated with the neural progenitor transcription factors and similar to the experiments I've shown you you can then go in and ask whether those elements are required so for example an element associated with a eventually expressed transcription factor NKEG 6.1 contains binding sites for the morphogen effector the uniform activator and for two neural progenitor transcription factors and when those are mutated you can see individually mutated within the context of the regulatory elements you can see the predicted outcome so for example removing the repressive input from the binds dbx results in an expansion of NKEG 6.1 whereas removing the socks or the glee elements results in the absence of or very much lower gene expression so this is all consistent with that idea that you have these descriptive regulatory elements so what questions do we want to answer so so far there's biochemical evidence for the glee and the socks family binding to those elements but is it also true that the neural progenitor transcription factors are also binding the bioinformatics would support that but is there biochemical evidence for this moreover we focused on the transcription factors themselves but is this strategy true for the entire transcriptional program of each of the progenitor domains not just the cross-regulating transcription factors and then finally how do you actually get domain specificity out of this how do you get those discrete domains of gene expression yeah and yeah they're not single processing and answer are doing much what I'm saying like you're the model before writing if you just assumes a very simple regulation probably right of the genes and then you can build this model to spare in the dynamics of the transcription factor you run it and it sort of you can think that the answer does do all that integration to give you the right response by really not doing much in the processing these dynamics we know of an example in which the answer is essential I mean it's so there has to be a molecular implementation of those of the network diagram but they're doing anything other than so for example think of the EVE strike I can just say whatever you don't have the depression and you have the other transcription that's what's on but is that transforming the signal in any order yeah so I think that's an interesting question right yeah so I mean this is this is the type of argument that I used to have with Eric Davidson because Eric Davidson was a proponent of the idea that developmental the logic of developmental gene expression had to be boolean so a gene was either on or off which is I think what you're implying right so these elements all they're doing is they're saying does the gene turn on or does it turn off so I think experimentally approaches have not been sufficiently subtle or sophisticated yet to answer that question I think over the next few years we'll begin to answer that with types of experiments where we can really precisely gene edit regulatory elements within the context of the genome so I'm not relying on transgenics or ectopic expression type experiments but where we're manipulating regulatory elements, deleting them or altering them in subtle ways and asking what effect that has on gene expression so that would give us a much more subtle read out than simple presence or absence of gene expression yeah I don't so in terms of signal processing what kind of thing are you thinking of what do you mean I mean it's not if I knew the dynamics of the prescription factor I could predict the dynamics of the downstream without knowing much about the architecture, how many binding sites are there, how much knowing the the geometry and the biogamy I don't know how much predicted power and how many are supposed to just put any function of the patient so I guess at what level of abstraction do you want to describe the system in so that high level the type of model I describe just gives you the I guess depends what answer you want to get yeah it's not binding that's activity so it says that so it says that sox and glee are required for activity that doesn't mean that other things are not binding to it okay let me push on so okay so to address these questions we've taken advantage of the of the we've taken advantage and I'll mention this again tomorrow but I've taken advantage of being able now to make large amounts of specific neural progenitors from ES cells so that allows us to do the kind of biochemical experiments that haven't been possible with embryos so essentially what we can do is take ES cells and then convert them a big plate of cells into progenitors which have the molecular characteristic of specific regions of the neural tube so now we have millions of progenitors in which we can do experiments so one thing we can do then is look biochemically at the binding of these key neural progenitor transcription factors and ask that question of whether we see biochemical evidence for interactions with specific enhancers I won't go into the details the answer is yes we can see binding at those regulatory elements so those elements bind glee, bind morphogen effect uniform activators and the neural progenitor transcription factors the other thing we can do now with this system is look at the entire transcriptional program of particular progenitor domains so not just looking at the individual transcription factors you're used to seeing but looking at the entire gene expression changes and define specific gene expression associated with each of those domains so ok so we've got three regions of the neural tube now in the dish so dorsal progenitors motor neural progenitors and the very, the NKX2 progenitor domain and we have gene expression for each of those domains plus the the evidence of the binding of those three inputs so how does, where does specificity come from so we can ask first of all whether there's any difference in the binding of the glee proteins and the socks proteins the morphogen input and the uniform input and the answer is there isn't so if we look at the binding of the morphogen input at genes which are induced in the neural tube whether they're in the p3 domain or the motor neuron domain 70% of the entire gene expression program binds the glee proteins and similarly many of those regulatory elements also bind to the uniform activator inputs so there's no obvious difference if we look at these two ventral domains about the positive inputs into into those domains so how do you distinguish how do you get a difference in the transcriptional program between those two adjacent progenitor domains and you can see that there's a substantial tens scores of genes that differentially express between those those two domains so okay so the obvious hypothesis is that to generate the green domain the nkx22 expressing p3 domain cells nkx22 is specifically expressing that domain and it acts to repress not only Olig2 but all of the genes which are uniquely expressed in those Olig2 expressing motor neuron progenitors so to ask that question we generated we in this case sorry I've taken a name of but ever pity over in the lab generated sets of ES cells where we can ectopically induce specific transcription factors such as nkx22 artificially using a drug induction system so now we have ES cells which we can differentiate into neural progenitors then independently manipulate gene expression within them so the experiment then to test this hypothesis is to convert ES cells into motor neuron progenitors and then artificially induce nkx22 in those motor neuron progenitors and ask what effect that has on the gene expression program and what we see if we do that comparing motor neuron progenitors to motor neuron progenitors in which we've induced nkx22 is that we now repress many of the motor neuron specific genes and many of those motor neuron specific genes have regulatory elements that bind to nkx22 so what that suggests then is for the motor neuron program and the P3 program both of the genes associated with those programs have binding sites have regulatory elements that bind the morphogen effector and the neural specific SOX genes but the motor neuron program is specifically repressed by nkx22 so in addition then so if you think about this these two adjacent domains but in addition you need to keep off all of the other domain specific expression within the P3 domain and we can go on to show that that is again directly by nkx22 so the P3 program those cells express nkx22 and one of the roles of nkx22 is to repress all of the other non-adjacent programs so everything that shouldn't be expressed in the P3 progenitor domain is being repressed by nkx22 okay when I say everything I've exaggerated a little bit so if we look at the induction of nkx22 it represses about 80% of the program but there's some genes which are not repressed by nkx22 if we look at the nkx22 domain it's co-expressing this other transcription factor nkx6.1 so we can do the same experiment now with nkx6.1 and what's really striking is the forced expression of nkx6.1 represses those genes which are not repressed by nkx22 and the combination of both now give us the full P3 program and again we can show direct binding okay so the combination of nkx22 and nkx6.1 is imposing a P3 transcription program by repressing everything that it shouldn't be expressed in the P3 domain so if we think about the motonewere progenitor domain now nkx22 is absent but in place of nkx22, Olic2 is expressed so does Olic2 replace nkx22 in repressing everything that shouldn't be in the motonewere domain and indeed it does the same experiments ectopically express Olic2 show that it inhibits the dorsal progenitor program and binds to many of those genes moreover if we look at where Olic2 the regulatory elements that Olic2 is binding then in 75% of the cases it's binding to the same element that nkx22 is binding to in the P3 domain so that suggests a model so remember nkx22 and Olic2 are not expressed in the same cell types but they do interact with the same regulatory elements to repress the same set of genes so there's and those dynamics of gene expression mean Olic2 is initially bound to those elements then nkx22 represses replaces Olic2 repressing the same set of genes so that comes back to this idea with in many cases the cis-regulatory elements of target genes contain a combination of neuro-progenitor transcription factor binding sites and it's that combination that allows the serial repression of the non-expressed genes within inappropriate progenitors okay so that's really complicated so this is my attempt to summarize that so if we think about the ventral transcription factor programs which are dependent on hedgehog signaling many of those genes have regulatory elements that bind to the morphogen effect of the glee proteins plus the uniform transcription factor so that is sufficient to induce expression within the ventral half of the neural tube domain specificity is then imposed by the neuro-progenitor transcription factors themselves repressing all of the inappropriate gene expression so you end up specifying domain specific gene expression through a derepression mechanism it's those things which aren't being repressed which define the domain of gene expression okay so in words this is my attempt to summarize that so the cis-regulatory elements those enhancement elements integrate multiple positive morphogen and uniform inputs plus multiple negative inputs those neuro-progenitor transcription factors the positive inputs are broadly activating so they're broadly activating many of the ventral programs and it's the repressors with select identity by inhibiting all of the alternative programs and it's the dynamics of the network which eventually generate the spatial pattern so another way of saying that is the morphogen is there activating all possible programs and it's the transcriptional network which selects the appropriate outcome for the position in the neural tube and that's based on this combinatorial mechanism acting through shared regulatory elements okay so that's all I wanted to say so I hope you know something a little bit about neural tube patterning now and just to try and sort of summarize the main points if we compare what I've been talking about in the neural tube and particularly compare that to GAP genes but also many other morphogen tissues I think you can come up with sort of three sort of principles here so you have morphogens are there providing gradients of signal which initiate tissue patterning provides some initial polarization but on their own they're not sufficient to generate the pattern they're generated by modular regulatory elements integrating multiple inputs to control target gene expression and then interactions, regulatory interactions between some of those target genes the transcription factors generate dynamics which eventually which the dynamics of which divide the tissue into a series of domains arrayed along that patterning axis and going back right to the first point I wanted to make yesterday the fact that we're seeing this repeatedly in different examples in different tissues where there are many differences and no evolutionary common origin suggests that these principles may well be general principles for how you pattern a tissue in response to a graded signal so these are only some of the people from my lab and some of the collaborators which have been involved in this work thank you very much