 Ok, go. Good morning. So that's actually a useful introduction because you've got decisions to make. And I want to talk about decision making. So what I'd like to do is talk about sort of two on-going projects in the lab at the moment and they sort of develop on some of the themes that I talked about over the last couple of days. I've talked a lot about the pattern formation and role of morphogens. I'm going to return to that in the second half of what I want to say. I want to start off by talking about this idea of developmental decision making and differentiation. How does a progenitor cell decide to become one or the other differentiated progeny? Byddwn ni'n meddwl y cyfle o'r cyffredinion chi wedi'i gael i'ch cyffredinion i'r ICU yn ddiddordeb ym Mhwyddi Fawr, ac mae'r rhagleniaeth ymddai gyda'r mhwyaf. Aeth amdano gael y cyfle a'r ddweud y gallwch chi'n cofnodd gyda hwnnw? I this work is of course inspired by the great American philosopher Yogi Berra who made this comment. So, how does sales take it? So, as a way of introduction, we got into this because of our interest in the spinal cord. So I just need to give a little bit of background on neural induction and then talk about the work that we've been doing. Felly, yma wedi ddifwng ymddangos fydd y cyfnod yn gweithio'r adrodd. Felly, y mynd i'r ddifwng y rhagleniaid yw'r ddifwng ddifwng yma, yn ddifwng gyda'r ac yn ddifwng y rhan. Mae'r ddifwng, mae'r ddifwng, mae'r ddifwng. Mae'r ddifwng gennych ddifwng, ddifwng cyllidau ddifwng. Yn ymdill, y system ddifwng ymdill yn ddifwng ymdill, ymdill, ydwng y ddifwng gyllidau ddifwng. Felly, ydych chi'n gweithio'r ffawr o ddysgu bywyddiadau bywyddiadau, mae'n ddigreffau arall y llai. Mae'r ideaau y pwysig yn y proses gaslligau yn ymdweithio'r tref yma, mhysydoedd, exoderm, a endoderm, a'r syniad sydd yn ymdweithiau yn ymdweithio'r dyfod ymdweithiau. Mae'r idea btwdd yn ei gweithio, i gweithio, i gweithio, i grwp hynny, i'r meddwl ar ysgrifwyr diwrnod yng nghymru Cymru i yn ymgyrchol Cymru yn ymgyrchol. Mae'r syniad yw'r syniad yw'r syniad yw'r dyfodol yw'r ectodol. Mae'r grwp sydd wedi'u gwneud o'r gweithio'r Ystyn Smyth yw Llywodraeth Cymru. Mae'r gweithio'r gweithio'r Llywodraeth Cymru o'r 10 o'r 15 oed yn ymgyrch yn ymgyrch yn ymgyrch ymgyrch, yn ymgyrch gyda'r freinigiaeth, gyda'r hunain'r cynhyrch gyrfaeth, llwythio'r cynhyrch yn ymgyrch yn yr unedlaeth o gyfrinigiaeth neu olygu. Rhaid o'r cyfrinigiaeth yn gyfrinigiaeth neu olygu. Grwp sydd yma o os syniad yma, persuadeb hwnnw yw'r gallu cyfrinigiaeth, i arwag y gallai cyfrinigiaeth yn cael eto iechyd i'u ffordd unigai'n deoliad. ac ar y peth o thredag, argynwch ar ogylchu'r cododi'r cymdeithas yr allan ynghylch yn gyfrif yn iawn o gyllid o gyfrif, ac yn cael eu cyfnod gyda sylwyddy i'r systemi nerfynu. Oherwydd, mae'n ddreifio sydd yn ychydig o'r cododi sorg o hyd ardalod y ddynnu o hynny arda'r ddynnu o'r d потрif. Be'i ddynnu certhydig o'r contiwyr. ac mae'r gymryd yn ydych yn y ddeudio gwir ychydig i amserion yn ymddangos. Felly, yma, a'r idea yn ymdweud yn y bydd y 20th yma, ac ymdweud ymdweud cyfan yng Nghymru Cymru, yw ddechrau cyfan yng Nghymru Cyfan yw Peter Nyuwch, yn y cyfan ynghylch cyfan ynghylch cyfan ynghylch yn ymdweud, yn ymdweud ynghylch yn y ddwyfydd ymdweud. ac mae'r syniadau adegwyddiadau yn ysgolwyddiadau y porwyr o'r tystiol i gyrraedd y rheswm y system ymlaen. Yr ystod y mecanysgau yn ymddiad cyfnodd ar gyfer Peter Newkip yw'r cyfnod o'r hynny o'r hyffordd o'r hyffordd o'r hyffordd. Yn ystod yw'r hyffordd o'r hyffordd o'r hyffordd o'r hyffordd o'r hyffordd ac mae'n ddweud o'r hyffordd o'r hyffordd o'r hyffordd o'r hyffordd o'r hyffordd. A sydd pobl yn ymgyrchεταιol, rodio'r gwineud o'rほw fodod o'r f ihremau a llunio cwmif��au covid am yr corfu golygu yn ysgolwyddiadau sy'n fwyb yn ddweud o hyffordd o'r prydyn ni. Rwy'n meddwl, dyma'r ddweud yn cael ei ddweud. Dyma'r ddweud o mynyrgyltid, sy'n ddiwedd yn rhai gynllunio'r llai. Rydyn ni'n ddweud o Austin Smith. Roedd y prydyn ni'n ddweud o'r prydyn ni'n rhaid, yn ddweud o'r cyfnod i'r prydyn ni'n ddweud o'r prydyn ni'n ddweud. Rydyn ni'n ddweud o'r prydyn ni'n ddweud o ddweud o'r roedd Felly, ydych chi i'n meddwl i'w 5 gynnal i'r cyffredinol iawn ar y cwylwyr, ac mae ydych chi'n meddwl i'u y hoffa ar y cyffredinol iawn ar y system gwahanol. Ydych chi'n meddwl i'w cyffredinol iawn ar y cyffredinol iawn, mae'n cyffredinol iawn ar y cyffredinol iawn ar y cyffredinol a'r gwahanol iawn ar y cyffredinol iawn. If she added retinic acid at day 3, this transformation signal, the posteriorising signal, asset day 5, then retinic acid will inhibit those anterior markers and instead will get more posterior markers, so markers such as the Efrens, Hoxby 2, Hoxby 1, which are characteristic of more posterior regions of the nervous system, specifically characteristic of the mid-brain and high-maj. However, what we found frustrating because we're interested in the spinal cord is that we were never able to generate cells with the molecular characteristics of the spinal cord. So, if we look at particularly the posterior hox genes, which are characteristic of the trunk and more posterior regions, then we never saw retinic acid being able to induce those molecular markers within in this protocol. So, it's frustrating for us because we're interested in the spinal cord. Also, the spinal cord is quite a lot of the central nervous system, so we really wanted to understand what was going on here. Yeah, so that was the idea here of adding, so this is actually from no to 100 nanomotor. I don't remember exactly the concentrations we've used here, so that's exactly the idea. Right, and we haven't looked into this in great detail, and the reasons for this is I will just about to explain. Okay, so the fact that we're not generating most posterior spinal regions of the nervous system made us wonder, so made us think more carefully about this, the activation transformation hypothesis. So, this is well established, this is the prevailing view in the field, but of course it's a simplification. It's sort of known to be a simplification, but it has largely been overlooked, I think. And in fact, this has been known, this idea of a single origin of the nervous system has been known to be a simplification for more than a century. So in fact, the first reference I found to this goes back to the late 19th century and the Swiss embryologist Albert von Curlaker. So in this period of developmental biology there was still sort of mid to late 19th century, there's much debate about whether the germ layer hypothesis was valid. And Curlaker was one of the embryologists arguing against the idea of a germ layer hypothesis. And one of his arguments is actually laid out in this paragraph referring to this figure, which is in his sort of collected works, this book of his collected works. So I'm afraid it's in 19th century German, but this is my attempt at translating that. And he's referring to this figure here, which is a beautiful hand-drawn diagram of the posterior region, the tailbud region of an embryo. And he says, quite strikingly, he says, in a sense a part of the nervous system is derived from the mesoderm. The spinal cord, after it's been created, is a closed tube away from the posterior end, but it merges with the somites and nautical nectaderm at the posterior end in the cell mass, which is primarily of the middle germinal layer. So here he's making an argument that the spinal cord is actually a product of the mesoderm, not of the ectaderm. So this really contradicts this currently prevailing view. So that was back in the late 1800s. He wasn't the last person to work on this, and there has been some subsequent work over the next century or so. But I just want to highlight the work of Valerie Wilson in Edinburgh who has really looked at this in much more detail using more modern techniques and finds really strong evidence for what Von Kulaka was arguing. So in several, in a series of papers in the early 2000s, she's demonstrated so by doing transplantation, so taking little regions of the tailbud from GFP expressing embryos, transplanting them into non-marked embryos and then looking at the progeny, looking where the GFP cells end up. She's found evidence that those transplants from that tailbud will indeed contribute to both the spinal cord and the mesoderm, as Von Kulaka was arguing. Moreover, in lineage analysis done between Val Wilson and Jean-François Nicolais in Paris, so marking individual cells in the early embryo and then looking at the progeny of the daughter cells of those much later. What they found is a group of clones that contribute to both spinal cord and mesoderm and no other tissues, and those tended to be relatively small clones, suggesting that the originator of these clones, the cell that gave rise to these daughters was a bipotential progenitor which went on to produce progeny that contributed to both those tissues. So these type of data and more supportive data as well leads to a revision of that simple lineage relationship, which in fact splits a nervous system into two lineages. So the anterior nervous system comprising the brain, so forebrain, homebrain, midbrain, has indeed derived from epiblastectodermal tissue. By contrast, the cells which contribute to the spinal cord appears to have a more common progenitor that is shared with prax and mesodermal cells, and I'm going to call this a neuromesodermal progenitor after the evidence from Val Wilson that in fact individual cells can give rise to both neural and mesodermal tissue. So this suggests a revision to that sort of simple lineage relationship that you'll see in most developmental biology textbooks. So we wondered whether this was also the reason why we were unable to make spinal cord progenitors from ES cells and we thought about where would this cell be in the embryo and what would this cell be doing. So if you think about the results I've showed you so far, this bipotential progenitor would be located in the tail bud of an elongating embryo. So this is a diagram of an embryo about E8, so that's sort of at the later time point you saw from Katz's movie of a developing embryo. So at that time the tail bud is beginning to, or the posterior of the embryo is elongating posteriorly and the NMP cells and neuromesodermal progenitors would be located in that most posterior region of the embryo behind posterior to where spinal cord, mesoderm, other tissues are differentiating. And that region of the embryo is exposed to Wintz and FGF signalling. So if we look more detail in this and this is a review from Dominguez Sanrique and Kate Story, if you look in an actual embryo I think this is a similar, this is just slightly older, E8.5. If you look in that posterior region of the embryo, so now this is posterior, the head would be somewhere up here. And this is marked with two transcription factors, so in green is SOX2 which is expressed in neural progenitors and in red is a transcription factor brachiori which is expressed in mesoderm and is normally considered to be the master regulator of mesoderm induction. So if you, these are cross sections at various positions along this, so if you look away from the very posterior end of the embryo you can see SOX2 in the forming neural tube and brachiori here is in the notochord SO which is a mesoderm derivative. If you look more posterior to that behind the node then you can see a region of tissue where you see cells co-expressing both SOX2 and brachiori. So if you look at cross sections through here you can find individual cells which are expressing both the neural marker SOX2 and the mesoderm marker brachiori which would be sort of a molecular collar would be consistent with this idea that cells have a bipotentiality, so they have some kind of superposition of both neural and mesodermal identity. Okay and this is the region here which is being exposed to wind and FGF signaling and crucially those cells are exposed to wind and FGF signaling before they've entered into either neural or mesodermal tissue. So Mina wanted to ask whether we could exploit that. If we mimic that in vitro could we actually generate neuromesodermal progenitors and then spinal cord. So that seeing what was going on in the embryo then allowed us to tweak to change what we were doing in the vitro differentiation. So in the normal differentiation not neural differentiation you release cells on pluripotency conditions and allow them to differentiate for three days. And it's that three day time point when neural markers begin to be expressed. So what we ended up finding is that if we expose cells to a pulse of wind signaling between day two and day three so prior to those cells adopting a neural identity. And if we assayed at that day three time point in contrast to the controls which express socks to the neural marker after the 24 hour exposure to wind signaling we see these differentiating cells co-expressing socks to and brachiori very similar to those cells we're seeing in the embryo. So that looks like they may be neuromesodermal progenitors. If we allow those cells to then differentiate further in vitro so we remove wind signaling at day three and then allow those cells to differentiate for two additional days. Either in the presence of retinoc acid or in the absence of retinoc acid in fact. Brachiori isn't maintained so brachiori is transiently expressed and then downregulated. However socks to is consolidated and then if we look at the progeny of those cells with a range of molecular markers we find evidence of differentiation into a neural tissue and indeed into neurons. And when we look at regional identity we find molecular markers characteristic of the spinal cord. So for example Hox C9 is expressed in the trunk the thoracic region so between four limb and hind limbs and you can see many of those progenitors expressing Hox C9 in those conditions. So that's consistent with this idea then so if we take ES cells and allow them pulse them briefly with wind signaling and then allow them to differentiate into neural cells they become spinal cord regional identity. So are they really going through this bipotential state so can we also direct them to become mesodermal? Sorry, are all of these progenitor cells bipotential cells? Not necessarily two cells it could be so I'm not saying they're doing an asymmetric division they just have the potential to become bipotentialities. So they have the potential to become either neural or mesodermal and I'm just about to show you that these cells we can also direct to mesodermal. So at day three remember they're co-expressing socks term brachiori so can we also direct them to mesoderm? And the answer is yes we can and we can if instead of removing wind signaling at day three we continue exposure to wind signaling from day three to day five. And now in those conditions we're calling mesoconditions then instead of upregulation of neural transcription factors such as a socks family those are downregulated and instead we see the upregulation of a set of markers characteristic of the praxe to mesoderms on a mesoderm that which would go on to form the sown lines. So most notably the T-box transcription factor TBX6 which is expressed through that region of the embryo you saw Andy looking at yesterday so the pre-semitic mesoderm is expressed by the majority of cells exposed to wind signaling at day five. And then if we allow those cells to continue to differentiate in vitro we can see molecular markers characteristic of cells which are normally derived from the sown lines. So Desmin and Myodi expressing cells which is a characteristic of mussel skeletal mussel cells. When your first lecture is talked about in the DC this is not the way that I scan if it feels like it's the one on the bottom. Yeah so this will yes I can so this pulse of wind signaling it has to be prior to day three which is a time point at which you see socks one come on which is sort of our marker for neural cells. So those cells are competent to become NMPs prior to day three when they're committed to a neural. But you also can't add wind too early and our interpretation of this again based on molecular markers is that mouse ES cells look molecularly closest to ICM cells that Kurt was talking about. And over this period of one or two days they lose some of the ICM character and adopt an epiblast like identity. Again this is based on molecular markers specifically by day two by between day one and day two those cells are expressing FGF five which is normally considered an epiblast marker and distinguishes from the ICM. So we think the key aspect is that you're exposing epiblast like cells to wind signaling and that's key for this posteriorization. And again if you think about where those cells are located in the embryo that's in a region that Val and others refer to as a quadrilateral epiblast so it's epiblast. So what we think we're doing here is as closely as we can recapitulating the normal signals that those embryonic cells would be exposed to. Okay and then finally just we can also transplant these cells so day three we can transplant them back into mouse ES cells back into chick embryos and they will contribute to both spinal cord and somites. So that's consistent with this idea then so we can in vitro now recapitulate the aspects of the development of the spinal cord, convert ES cells to neuramesodermal progenitors which we can then direct either to mesoderm or to spinal cord progenitors. So this so far just talked about mouse ES cells. We can use the same principles and this has been done in collaboration with Ernestas Dacarides in Val Wilson's lab. We can adopt the same principles to convert human ES cells to NMPs and then to progeny of NMPs. And again this comes back to the question about the timing so human ES cells appear to be a different embryonic stage from mouse ES cells so they're more similar to epiblast rather than ICM. And what we found is that we had to change the timing of the addition of signals to account for the different slightly more mature identity of human ES cells. But with that change then we can generate cells, human neuramesodermal progenitors with many of the same molecular markers as mouse NMPs. I think this is interesting as a developmental biologist because these kind of approaches for the first time allow us to think about doing human developmental biology so we can start to recapitulate aspects of human development in vitro. The other point I wanted to make is sort of the evolutionary point. So if we think about this population of neuramesodermal progenitors in vertebrate embryos, they're located at the posterior tail region of the embryo and they contribute progeny that generates both neural and mesodermal tissue under the influence of wind signalling and through transcription factors such as CDX caudal which you'll hear about. If you think about other bilaterians, so you're not Drosophila because Drosophila is weird, but if you think about all other, most other bilaterians, then there's a very similar mechanism which generates a trunk of almost all bilaterians. So a population of cells of the posterior end of the growing embryo referred to as a growth zone in insects, in short germ-bound insects. Also contribute cells to neural and mesodermal tissue under the influence of the same signals, under the influence of wingless signalling and indeed that region of the embryo expresses the same set of transcription factors, the caudal. So this population of cells, this mechanism is probably ancestral to bilaterians and Drosophila is unusual in being a long germ-bound insect in which the whole AP axis is generated simultaneously rather than being sequentially laid down by axis elongation. So wingless signalling is well established as a posteriorising factor, so the history of molecular embryology identified wingless signalling. I should say this is a nice review from David Kimmelman on this, talking about wind signalling and posteriorisation. So wind and wingless signalling is associated with posterior regions of not only bilaterians, I think it goes even in Nigerians as well, you can see evidence of. So it's a very ancestry, very evolutionary, deep relationship between wingless signalling and the posterior, the embryo. So I come back and talk about retinoc acid. So retinoc acid is, so that's much more vertebrate innovation as far as I'm aware, so certainly Drosophila you don't see retinoc acid. Who's working on planarians? I don't think there's any evidence for, is there any evidence of retinoc acid signalling in planarians? Does anyone know? Not that I'm aware of. OK, so where we got to? So we're now, we can return back to this decision making question, right? So we've now managed to establish an in vitro system where we can generate a bi-potential cell type, which we can direct into either, to progeny either into spinal cord or mesodermal cell types. And indeed we can find conditions in vitro where we generate a mixture of those two cell types, so proportions of both neural and mesodermal cells simultaneously. And those will actually go on to differentiate into neurons which really want to synapse onto the muscle like cells that are developing in vitro. So we thought this was a good system to try and ask what is the underlying mechanism that allows cells to decide between two alternative phase. And we've taken several approaches to this, so the one I want to talk about today starts with some analysis of single cell transcriptome data from these. So again this is in collaboration with Val Wilson's lab and we've done this from both in vivo and in vitro cells. I'm just going to talk about the in vitro data today. And I know next week you're going to have more single cell data, more single cell technology talks from Alan Klein. So this will just be sort of a brief warm-up for that. So the data I'm going to talk about comes from in vitro. So we've differentiated cells in vitro in conditions that give us a mixture of NMPs, neural and mesodermal cells. And then we dissociate those into single cells and then we're using a particular technology, a microfluidics technology which allows us to manipulate those cells into micro wells in which we can then perform reverse transcriptase and library synthesis. And this is a Fluodime C1 system. So we can convert single cells into CDNA libraries and then sequence those CDNA libraries and then align those to genome, normalise them, clean up the data. So remove debris, remove occasions where we have multiple cells and then analyse the data. So if you just, if you go through this pipeline you end up with transcriptomes for each of the cells you've sequenced. And then we can do things such as cluster that data. So here we're looking, so each column represents a single cell and each of the rows represents a particular gene. So we have, I think in this data set there's 100 or 150 cells in which clustering, so this is a hierarchical clustering. You can readily see that we've got several quite distinct cell types within this population. And indeed if we look at the gene expression signature for each of those cells we can begin to identify what those cell types are. So for example I know that this pink cluster represents neural progenitors within the population because we can look in, look at the transcriptome and see the expression of neural genes. Okay, so from the transcriptome data we can recover the identity of individual cells. But what we really wanted to do is ask whether we could reconstruct differentiation pathways. So the trajectories that take you from NMP to either neural or mesodermal cells. So to do that we've adapted some graph theory approaches that have started to be commonly used in this field. And this is based on Cole Trapman's work from a couple of years ago. And let me give you intuition here. So each of those cells is now represented by its transcriptome. So you can think of that as a very long vector of gene expression levels. So what we want to do is, so each of those cells is then a point in high dimensional space. Each of those dimensions being a gene. And so the idea is that the differentiation route would be, you would link cells to their nearest neighbours in that high dimensional space. So if you're close in high dimensional space you're related to one another. And then what you want to do is find trajectories, so minimum spanning trees from that very high dimensional graph. With the idea that minimum spanning trees, those minimum spanning trees would represent average differentiation routes through that gene expression space. How is that? Did that make sense? Without any template information at all. There's no template information. There doesn't have to be any template information at all. You're just assuming there's a synchrony within the population. So you're recovering cells which just happen to be close to each other in that temporal dimension. And you're trying to recover that, those relationships. Yeah, yes. So let's try, okay, so the idea is what we want to do. So each of these points represents a cell and they're connected by, because they're close to each other in that high dimensional space. And then this has been projected down into two dimensions. So let's try again. So here's the actual pipeline that Julian in the lab developed. So we have the transcriptomes of all of those cells. So what he does first is just to pick genes which have high variance. So we're not interested in genes which are constant across all of those cells. We're just taking the most dispersed genes with the idea that that would give us information about the differences. Join differentiation. And then we're measuring, he's measuring the distance between each pair of cells with a Euclidean distance based on the dispersed set of genes we're looking at. So then we have a matrix with Euclidean distance, pairwise Euclidean distance in which we want to reconstruct a graph from that. So one of the problems of course, when you think about this in high dimensional space particularly, and the technical noise which comes from inevitably from single cell transcriptome, is that it could be very sensitive to noise. So just a small change in position of an individual cell within that high dimensional space could lead to a very different graph. So to try and deal with that, he's taken sort of a bootstrapping approach where he's building multiple minimum spanning trees but using only 80% of the data in each of those spanning trees. So you build thousands of minimum spanning trees from different selections of 80% and then you look at the edges which are commonly used and you just keep those and edges that are infrequently used, you eliminate. So from that you end up with a graph of connected cells and you can see minimum spanning trees through that space. So here this is a set, this one here, this is some distance measure. So I suspect that yellow means close and blue means far away but this is really just for illustrative purposes. So I should sort this out shouldn't I? So I think in here what he's illustrating, I do know. In here what he's illustrating is the red points here are the 20% of connections that he's not allowing to be used. So you're using just 80% of the data in each of these cases to build a minimum spanning tree and then each of the minimum spanning trees that you've generated, you compress all of those matrices into one matrix and you just keep the edges which are used in many of the spanning trees. So it's a bootstrapping wire trying to deal with sensitivity to noise. So it's a minimum spanning tree so what we're trying to do is to make a connected graph with the minimum number of edges or the minimum length of edges. Exactly. Well what we actually want to do is, so what we're assuming is that within this differentiation you have cells at every position along this differentiation. So both cells which are still in an NMP like state as well as cells which are going towards metadermal, going towards neural. Yeah and again we can look at the overall transcriptome of each cells, of each of the cells and determine how many large clusters there are and whether there are outliers within the population. Yes, yes, in fact you'll see that when I show you actually. Okay, so when we've done that right, so we've started off with this population of single cells and then this is the graph we end up with and again I've coloured, so each of these points represents a cell and this graph is based on that minimum spanning tree reconstruction and I've coloured these cells on the basis of the clustering here. So what you can see is that the clusters are close together in this graph, so that makes sense. That's what we want to achieve. In addition what you can see is that there's obviously two branches to this graph and I've already labelled the different populations here and I can label them because each of these cells, we know the transcriptome and we can look at the gene expression in each of those cells and based on the markers we're familiar with, we can identify those populations. So for example, so just in more detail then, if we look at the expression of this set of transcription factors, so remember that SOX2 is expressed in NMPs and in neural cells, Brachiori is expressed in NMPs and mesodermal cells, so you can see this population of cells here is co-expressing both SOX2 and Brachiori. Along this branch here you see decreasing levels of SOX2, but Brachiori is maintained and you see the upregulation of TBX6 and TBX6 is that marker for paraxial mesoderm. By contrast, if we look along this branch here, you see a downregulation of Brachiori, an upregulation of SOX1 and SOX1 is a marker for neural progenitors. So that suggests that this graph technique has appeared to reconstruct the trajectories from NMP to neural and mesodermal and now since we have the complete transcriptomes of each of those cells, we can look at the average changes in gene expression along each of those routes. Does that make sense? If we do that then, so if we go from NMP to neural, we're looking at the average level of expression of genes from NMP to neural along that trajectory. If we look at a broader range of genes here, in the NMPs we see Brachiori and SOX2 expression, also another transcription factor known to be expressed in NMPs in case 1.2 and they're called all the CDX family of transcription factors. And then as you differentiate towards neural, you see the upregulation of things like SOX1, Iroquas 362, downregulation of Brachiori and the CDX family members. By contrast, if we look along this trajectory from NMP to mesoderm, again we're starting the same position so we see Brachiori, SOX2 co-expression. As we move towards mesoderm or SOX2, we see the downregulation of SOX2 and upregulation of things like TBX6 and mesogenin, again characteristic of mesoderm. So from the single cell transcriptome data, we can begin to infer these differentiation trajectories which also suggest regulatory relationships. So it's quite noticeable that you're beginning to see anti-correlation between some of these transcription factors. So we wanted to ask whether we could use these data to go one step further and reconstruct the transcription network which produces this bifocation, produces this decision. But to do that, we wanted to not only use this correlative data but to perform perturbations to really test the potential genetic interactions. I want to use the next couple of slides to highlight why I think performing this in ES cells, directed differentiation of ES cells has certain advantages over doing this in whole embryos. First of all to illustrate that, I'm going to take the example of the CDX family of transcription factors. So there are three CDX transcription factors in mammals. They're all expressed as you saw in the posterior of the embryo in NMPs. They've been implicated in the generation of the trunk of the embryo. But this is quite technically challenging work to do. First of all, there's three genes which you have to knock all three of them out of mouse embryos and Jacqueline Duchamp has done this. But then the problem is so you knock out the three CDX genes and you end up with a truncated embryo. So the embryo forms the first five or six somites and then there's no more tissue. So it clearly says that CDX is required for access elongation for the generation of mesoderm and spinal cord. But because you've got no tissue it doesn't give you much more insight into molecular mechanism. So the advantage of ES cells and differentiating ES cells in vitro is that you're not reliant on the rest of the embryo in order to analyse what their function is. So we've done this with the CDX genes so we can make ES cells using CRISPR that lack all three CDX genes and then use those in vitro differentiation protocols to convert those CDX null cells into either neural or mesodermal cell types. So here what I'm showing is either wild type or CDX null ES cells differentiated using the mesodermal differentiation protocol and then assayed for neural markers. So because we're differentiating to mesodermal tissue wild type cells don't generate neural so not expressing neural markers. By contrast however in the absence of CDX these cells now adopt a neural identity. So that suggests that CDX proteins, the CDX genes are required for mesodermal induction. So not only are they required to maintain access elongation but they're actually in addition required for the specification of mesodermal tissue. The other thing that you can do in vitro is much more easily than you can do in vivo is manipulate the extrinsic signalling conditions. So I've emphasised the idea that winter FGF is required for the induction of NMPs. So as we've already discussed retinoc acid is also being produced in the embryos actually being produced in the somites. And there's a question of whether retinoc acid, what role does retinoc acid have if any in the generation of NMPs themselves. And again we can ask that question by manipulating retinoc acid signalling levels in vitro. And so what we found is that if we remove all retinoc acid, so all vitamine A from the differentiation then SOX2 is no longer maintained. So if we look at day 3, SOX2 is no longer expressed in vitro and instead you have high levels of brachiori and actually a more rapid induction of TBX6. Suggesting that SOX2, in fact low levels of SOX2 within the NMPs themselves is required to maintain neural competence, required to maintain SOX2 expression. So if we put that together then we can begin to start reconstructing a transcriptional network. So I've talked about several of these transcription factors, the kind of experiments I've described together with existing knowledge from the literature allows us to begin to put this together in a transcriptional network in which wind signalling is promoting metaderm identity and retinoc acid neural identity. So as I talked about yesterday, the next step we wanted to take is can we look at this, can we start to think about this as a dynamical system. So we've taken the same strategy as with the neural tube, tried to boil down this network to the minimum possible to explain this bifurcation behaviour. Converted it into a series of three linked differential equations and then performed another optimisation. So asked for parameterisations of this network which give us back the appropriate behaviour again by optimising this to several different targets where we've manipulated either signalling conditions or simulated mutant conditions. So it's very similar to what I described yesterday, still very much work in progress but we can again recover parameter sets that perform appropriately and then we can start to look at this behaviour in silicae. So one thing we've done then is to look at this behaviour and assume that there's some level of stochasticity. So introduce some noise into those recovered dynamical systems. Again looking at the behaviour in one of these plots where we're looking at SOX2, Brachyur and TBX6 and challenging in silicae the simulations with different signalling levels. We can start to recover what you can think of as a decoding map in which behaviour in response to different levels of wind signalling and retinoc acid signalling in silicae. So as you might expect, wind signalling favours mesoderm, retinoc acid signalling favours neural and we can begin to see predictions for combinations of neural and mesodermal tissue with different levels of wind and retinoc acid signalling. And remember that's what we're seeing from the in vitro conditions and in vitro now we can manipulate the concentrations of wind and retinoc acid signalling and really look at the relationship between the proportions of cell types we're generating in vitro and the proportions of cell types predicted in silicae with the ambition that we should be able to constrain the parameters quite considerably. We should be able to get a much better idea of the parameter sets which generate the appropriate decoding map. So I think, so save that question for Alon Klein next week so he's really an expert in that so he'll be able to and I'm sure he will go into some detail about that. Something we discussed. Right because this decoding map you have, that's not any dynamics you showed in a couple of days. Yeah, so we do have this, sorry, this is meant to be the dynamics. I'm not sure I can answer that without thinking about it more. But you haven't tried I guess. No, no. I mean so part of the reason for this is that our actual, well first of all we like, it's nice using continuous functions because there's a lot of theory. But also the optimisation actually we're looking, part of the optimisation is for levels of, so for example we know, so SOX2 levels are lower in the NMP condition so that was part of what we were optimising to take. We don't know the answer to that. We tend to ignore cell cycle. The cells are proliferating during this and whether there's, whether and how cell cycle influences this we haven't looked at. But it is a key between the fact that over many cell cycles there are many narratives of the drugs. Yes, I mean there has to be an inheritance unless there's a mechanism specifically stopping inheritance. So the default assumption would be a Poisson distribution of transcription factors between daughters unless there's some mechanism to stop that. Right, so this colour, so yellow is NMPs and we're defining NMPs as having moderate levels of SOX2 and above a threshold of brachiori. The grey are unassigned and they represent within the simulation cells which don't fall into the thresholds we've set to define these different cell types. But this is very much work in progress and this is refining the simulations on the basis of data that we can generate from these type of experiments is exactly what we need to do. Okay, I'm going to skip that. We're beginning to get to a point where we have a transcriptional network that we convert into a dynamical system to explain this behaviour. So there's one thing that I didn't mention which I think is interesting as well. So retinoc acid is being produced by the somites which is a mesoderm derivative and retinoc acid is promoting neural induction. So if you think about this then there's a regulator feedback through this and we can sort of summarise that if we abstract it down to this kind of network. So mesoderm induction dependent on wind signalling induces TBX6, TBX6 expressing cells produce more retinoc acid, retinoc acid is favouring neural induction. So if you produce too much mesoderm then that will result in more retinoc acid production which would then favour neural generation. Conversely, if your production of mesoderm decreases you'll produce less retinoc acid therefore produce more mesoderm. So this is actually looking at Cat's recent work as well. This sounds very similar to the mechanism generating ICM, from ICM generating epiblast and primitive endoderm. So remember that epiblast is producing FGF and FGF is favouring primitive endoderm. So this is a very similar regulator feedback strategy to that Cat is talking about. So it provides a way of balancing the generation of two cell types. So if you think about this in the context of access elongation you need to be making the right proportions of neural and mesodermal tissue to have the well-regulated elaboration. So if you're producing too much of one tissue then your access elongation will fail. So this may be again a recurring theme in these systems. So a regulator feedback that rebalances the production of cell types if they become unbalanced. Otherwise isn't that when it's under certain condition they have pipe out them but then at one stage it's favourite, doesn't it? It's always on one stage. In a model or in... Yeah, so I'm pretty sure we would be able to find that in a model. What I'd like to do is get a more constrained parameter set first which we feel is better representing the data. It is true, so exactly. That is true, so in fact... So in some of these conditions... So this will be, yeah, the bifurcation parameters will be wint and retinoc acid in fact in that case, yeah. Okay, so now I want to switch gears. So how are we doing on time? So I wanted to switch gears now and come back to neural tube patterning. And so I talked a lot about neural tube patterning and I talked about just this little area down in the ventral neural tube. So now I want to take a slightly different perspective and think about the whole neural tube patterning. So as I introduced to you, neural tube is patterned along this dorsal ventral axis and is patterned by anti-parallel gradients. So we've spoken a lot about hedgehog signalling ventrally but dorsally BMP signalling is important. And BMP signalling in a mirror image to a hedgehog signalling divides the dorsal neural tube into domains of progenitors. So this idea of anti-parallel morphogen gradients is a recurring theme in tissues. So the other common example would be anti-parallel gradients of bicoid and caudal along the AP axis of the drosophila embryo. So how do anti-parallel gradients, if we think about this at the tissue level, what's the strategy for patterning with anti-parallel gradients? And one additional complexity, particularly in the case of the neural tube or particularly in most tissues, the drosophila embryo being unusual in most tissues, this process of patterning is happening as the tissue is growing. So this is just taking some representative images across this developmental time window for the neural tube from early to late. So this is about a 48-hour time window. So you can see over this period of time the neural tube, the patterning axis, grows by three to four-fold over this period of time. So there must be some mechanism that allows the pattern to be elaborated even as the tissue is changing this markedly in size. So how do anti-parallel morphogen gradients, how do they fit into this? The starting point for this piece of work was just looking at these images, noticing the growth in the tissue and noticing the gradual elaboration of this pattern, but also looking at these domains and thinking that these domains look consistent. They have sort of a, the precision of these domains appears to be constant, relatively constant throughout this period of time. So it doesn't appear that you're starting off very noisy and refining. They always appear to have relatively constant precision. And we can be more quantitative about that. We can actually measure the precision of pattern over time. So this is taking two particular boundaries. So pack three, which is in the dorsal neural tube and NKX 6.1 in the ventral neural tube, looking at the precision of the boundary during this period of time we're interested in and seeing that throughout the whole time the precision of boundary stays constant, stays within about two to three cell diameters. Okay, so now we can ask the question, so how does that level of precision, how is that established? So within the framework of morphogens, we can ask the question of whether those two morphogen gradients, do they have enough information? Is there enough information in that gradient to account for this level of precision across this developmental time window? So we think about the precision of a gradient, so the intuition here is that if I tell you a concentration of morphogen, how accurately can you tell me the position within the tissue? So if the gradient is steep, then you have high precision. So a small change in the concentration will result in a change in position. By contrast, if the slope of the gradient is low or non-existent, then concentration information is not very informative. So a concentration at this, this concentration here could imply any position in this region of the tissue. And we can state that formally. Okay, so we wanted to ask what is the positional error, the positional precision provided by the hedgehog and the BMP gradients? And to do that, we don't want to measure the ligands, remember it's all about what's going on in the nucleus, so we wanted to measure the signal itself. So to do that, for hedgehog signaling, we've taken advantage of the reporter I mentioned yesterday and the day before. So a transcription reporter of Glee activity, the effector of hedgehog signaling. Whereas dorsally BMP signaling were able to use a readout of activated SMAD signaling, so the transcription effector of BMP signaling, so phosphose SMAD antibodies. So now this allows us to measure the gradient of hedgehog and BMP signaling over time. So first of all, measuring the hedgehog gradient. So the blue line here represents the Glee activity from ventral to dorsal. Each of these graphs is early to late, so early developmental time to late developmental time. So hedgehog signaling is active ventrally, so what you see is high levels of hedgehog signaling ventrally, a gradient of Glee activity decreasing dorsally and little if any Glee activity in the dorsal neural tube. And what you can see if you look at this is that the effective range of the Glee activity, the hedgehog gradient decreases over time and that's a consequence of the neural tube increasing in size. So your patterning axis is increasing in size and consequently your signaling gradient is being restricted closer to the source. So with those measurements of Glee activity, we can then measure the positional precision and that's the black line here. So you can see where you've got a steep gradient, you are reasonably precise, so you're precise within about two or three cell diameters and as the gradient retracts ventrally you see the region of precision decreases over time. So hedgehog signaling is high precision ventrally, so that's kind of intuitive. Can you hold on to that because I am going to hopefully get to some dynamics at the end. So then we can do the converse of this, so looking at the BMP and we see the opposite, right? So BMP signaling, smad activity is high dorsally decreasing as you move ventrally, therefore the precision is high dorsally, the gradient decreases, retracts over time because of the growth of the neural tube. So BMP has high precision dorsally. So we've got these two opposing gradients, so how precise with the neural tube, how much information is there if the cells were using a combination of those two gradients. So what's the joint positional precision? So you can calculate that, so if cells are using a combination of both BMP and hedgehog signaling, what you see at these early developmental times, the black line represents the calculated precision, you see at these early developmental times you have relatively high precision across the whole axis, including the middle, and that precision is about two or three cell diameters across the whole axis. As the neural tube grows and the gradients retract, then you see increasing imprecision implied by the gradients in the middle as those cells are no longer exposed to either the BMP or hedgehog signaling. Okay, so that makes some predictions or implies several things. So if we hypothesize that the gradients are providing the necessary precision to explain the sharpness of those boundaries, then what is the mechanism by which cells are integrating both BMP and hedgehog signaling? In addition, there must be a mechanism which allows the early precision to be elaborated at later times when the information from those gradients is declining. So first of all, this implies that cells are reading a combination of BMP and hedgehog signaling. And there was already evidence to support that. So, actually, some work I did, just as I was leaving my postdoc, suggested that. So this is by Carol Lee, my colleague of mine when I was a postdoc. And what we showed is that, so using chick explans, remember these neural plate explans, we can culture ex vivo, in the absence of adding anything that express markers characteristic of the dorsal neural tube. If we add hedgehog, then we repress dorsal identity and get ventral gene expression induced. If we add a combination, that same level of hedgehog signaling, but add BMP to it, now we repress a ventral identity and instead return to dorsal identity. So that suggests that cells in some way are able to, are integrating, receiving both signals or can respond to both signals simultaneously. OK. So then, if we think about this then, so we've got a patterning axis here of ventral hedgehog gradient dorsal BMP gradient. So we can now think about this patterning axis as a map or some kind of signal space in which one of the axis is BMP signaling, the other axis is hedgehog signaling. Now this patterning axis becomes a curve through this signal space. So in the ventral neural tube you see high levels of hedgehog signaling, low levels of BMP signaling. In the dorsal neural tube you see high levels of BMP signaling, low levels of hedgehog signaling. And these points along this curve represent equidistant positions along the dorsal ventral axis. So you can think of this as some kind of morphogen signal space in which the patterning axis is a curve through that space. So this curve represents the average levels of BMP and hedgehog signaling that a cell would see at each of these positions. But of course the reality is that because of noise, because of the vagaries of development, then in fact some cells will see levels of signaling that fall outside this curve. So you can imagine that they might see a slightly higher level of BMP signaling compared to hedgehog signaling be outside the curve, or down here they're seeing lower levels of hedgehog signaling compared to BMP signaling. So if a cell is exposed to that those conflicting instructions how do they decide what identity to adopt? So just looking at that the intuitive thing to do is to figure out what is your shortest distance to the patterning axis curve and choose that identity. So you would just figure out what's the shortest distance from your conflicting information back onto the patterning curve. And in fact that represents the statistical equivalent of doing a maximum likelihood estimation. So we can formally state that. So if your task is to infer position from measured levels of hedgehog and BMP so some level of BMP some level of hedgehog signaling if the average observed signaling levels at any position at a particular position X along the patterning axis is CB and CS if we assume that the probability of observing any level of those signals at that position is Gaussianly distributed so it's a bivariate normal distribution then you can write down just a bivariate normal distribution in which given a position your probability of observing this concentration or level CB and level of CS is given by this formula. So the task we want to do is the inverse of that is given to concentrations we want to infer X estimate give us a maximum likelihood estimation of X so that's just maximising the inverse of this. Okay, so we can calculate that given the patterning curve we've observed the positional identity that would be adopted by a cell given any combination of signals to which they're exposed so we can think of this now as a prediction we've converted the data we've measured hedgehog and BMP levels into a decoding map which represents any combination of BMP and hedgehog signaling so can we test this prediction? So the way to test this is we want to look at how cells are behaving if they're exposed to concentrations outside of their normal patterning axis and for the sake of time I'm going to skip over the first test and just take you to the second one. Okay, so the first thing was just talking about down here that fulfills the test on such a stringent test what was more interesting to us is thinking about this top right hand corner of the decoding map so in this region of the decoding map then there are two predictions so first of all if you're exposed to high levels of both BMP and hedgehog signaling the prediction is that you should lose intermediate positional identities so you won't become an intermediate cell so it's not like the cells are measuring the ratio of the two signals the second prediction is that in contrast to most of the decoding map which gives you unimodal probabilities of cell identities in this region of the map up here you begin to see bimodal distributions where there's almost equal probability of becoming either a very ventral or a very dorsal cell type so this provided us two predictions that we could test and by taking advantage of this x-plant assay so we can x-plant out this region of neural plate and then essentially recreate an in vitro decoding map where we are controlling the recombinant concentrations of those two signals so what you can see then we count in the number of cells expressing ventral or dorsal markers so nkx22 is a high response to hedgehog signaling you can see it's induced by high concentrations of hedgehog olig2 is induced predominantly by moderate concentrations of hedgehog whereas pac7 is a dorsal gene induced by BMP signaling and so from this we can look across this entire concentration map and we see in this top right-hand corner now in contrast to low levels of both BMP and hedgehog signaling where we get intermediate identities at this high concentration when they're exposed to high levels of both signals they lose intermediate identities and in fact show a bimodal response and you can see the bimodal response most clearly in individual x-plants where here we're looking at cells at x-plants exposed to high concentration BMP and hedgehog signaling looking at olig2 and pac7 and you see a mixture of cells expressing high response genes to BMP, pac7, high response gene or moderate response genes to hedgehog olig2 but most of the cells are decisive they're either red or green there's a bimodal distribution yeah so that's in fact so equal so you've got to think about this in terms of biological units I guess I don't think we would compare absolute concentration because they're activating different signaling pathways so if you think about the response of cells in the absence of the other signal I guess we don't have much here on the BMP but we've titrated the concentrations of hedgehogs so that in the absence of BMP it's giving us that ventral graded response and similarly with the BMP we're seeing different levels of response okay so these type of data suggest we've got a phenomenological model here so we can convert the dorsal ventral axis into a morphogen space of BMP and hedgehog signaling and this predicts how cells will respond to those two signals so it's a phenomenological mechanism with sort of essentially saying that cells are doing the equivalent of a maximum likelihood estimation so how do cells do statistics yeah so can we try and if you can serve the instantaneous concentration that I'm valuable I mean are you giving this back so the coding map is based on the measurements at one particular time point we can so the coding map will change slightly but not substantially if we take it from any of those early time points where we still have sufficient position information in the centre so if you let me talk about the transcription network this may give an answer to come back to sort of a molecular mechanism that can explain it so the hypothesis is that it's a transcription network that does it and okay so what's the evidence for this again we're going to take the same kind of root of reconstruct a transcriptional network turn that into a set of equations and then look how it behaves and so in this case we're looking across the entire dorsal ventral axis and for for the sake of the model we're going to look at three transcription factors that allow us to define three regions of the neural tube so nkx6 which is expressed eventually in the neural tube dbx which is expressed in a population of the main of progenitors in the intermediate neural tube and msx which is expressed dorsally so the type of genetic evidence I introduced yesterday we've also taken advantage of here so for example in when we knock out both nkx6 genes we see that dbx expands ventrally indicating that nkx6 is a repressor of dbx so if we take those type of data we can begin to we can reconstruct a genetic network comprising those three genes which for simplicity I'm going to call ventral, intermediate and dorsal there's a series of cross repressive interactions which should be familiar to you from yesterday between those three transcription factors and then we hypothesize that the ventral and intermediate gene might have input from hedgehog signaling whereas the dorsal and intermediate gene might have input from BMP signaling so with this topology we wanted to find sets of solutions that back the decoding map so to do this again we've taken an optimization approach to it and so in this case because we wanted to think about the dynamics in fact our input into this wasn't a single time point it was actually the data of the gradients through the time course we're looking at so we're actually using the data itself slightly idealized so we've fitted these but we're using the data itself over time as the signal input into this and then the screening criteria we're looking for is to explain the gene expression patterns to give us some of the perturbations I didn't show you to recapitulate those and then to give us back the decoding map that we're seeing from experimental data so again it's an optimization approach so there's 13 parameters in the model we started with I think 600 million parameter sets take it through a series of criteria and we end up with about a thousand from those 600 million parameter sets we end up with about a thousand that pass each of the screening criteria so if we look at those the thousand that pass those criteria then I think something like over 99% of those we can smoothly interpolate between those suggesting they're representing a single single region of parameter space so we have a set of parameters that pass the screening criteria and now we can look at how how they're behaving so this is just taking three of those parameter sets these little pinwheels illustrate the values of those 13 parameters so if we look at the just the behavior of the gene expression across the dorsal ventral axis they're giving us the appropriate stripes of gene expression moreover they're giving us the dynamics of gene expression we're seeing from the experimental data and they're giving us back a decoding map that looks very similar to the decoding map we saw experimentally with this particularly looking in the top right hand corner this loss of intermediate identities this acquisition of bimodal distribution so then with those thousand parameter sets which are performing the task we can ask what is common between those parameter sets so can we understand anything about the mechanism if we look at those parameter sets so there's two sort of key things two things in common between each of those parameter sets the first is that all of the cross repressive interactions between bimodal distribution are necessary so sensitivity analysis suggests that if you you can only change the cross repressive parameters a small amount before you break those systems in addition if we try an optimization where we forbid one or more of those cross repressive interactions we don't recover any parameter sets which pass the screening criteria so the cross repressive interactions are necessary the other thing that is that is obvious is that while B&D require morphogen input the intermediate gene either requires either weak input from the morphogens or no input at all so the intermediate gene is actually induced by default so in fact what happens and that's so that requirement for growth is necessary so in the successful models here what is happening is that initially the morphogens are inducing the V&D genes but as the gradient retracts to the poles then that decreases the level of signaling in the intermediate allowing the intermediate gene to be induced which then has repressive interactions with the V&D gene so does this explain that other observation that we have high precision high positional information early but later on there's no longer high positional information so can we explain how you use that positional information early and then maintain it at later times and again you won't be surprised given the number of cross repressive interactions there's lots of bi-stability within this network and indeed in silico we can ask we can remove the signals at particular times and ask whether we can maintain the decoding map so in essence if we look at the decoding map at 60 hours at the end of the run this is all at 60 hours if we give them signals up to 60 hours they have the full decoding map even if we remove the signal at 30 hours we can still maintain that decoding map even at 15 hours it's reasonably good so you only need the signals for the first 15 to 20 hours in order to generate that pattern and then it becomes and it maintains itself through the bi-stability from the cross repressive interactions okay we're done so this is the summary so anti-parallel gradients are patterning the tissue the cells appear to be integrating both of those signals and they're performing the equivalent of a maximum likelihood estimation at their position we can illustrate that with that decoding map that I showed you and we can also so that's sort of a phenomenological model we can also recover that with a mechanistic model of a 3 node transcriptional network suggesting a mechanistic explanation of a phenomenological model and importantly that that result separates the early gradient decoding from the later maintenance pattern suggesting how you can have precise patterns maintained even in growing tissues so what that's suggesting is this sort of two phase mechanism for establishing pattern so an initial period of time anti-parallel gradients are providing position information establishing position identity within the neural tube so that's at the time when the tissue is smallest allowing the maximum range of those two signals over time that pattern is consolidated through the bistability in those toggle switches and then it's elaborated during a subsequent growth phase of the tissue why not scaling up the tissue I mean either you have a uniform growth and that's the way you repeat but otherwise you've got to change the proportion yes and yes I have a lot I have another talk about that yes so so yes you do I mean you can notice that proportions don't say the same so for example this domain here gets smaller relative to the other domains this is in fact the somatic motor neuron producing domain these cells differentiate much more rapidly than other neural progenitors within the tissue so in fact this I'm not sure if you want to call it scaling or not but there's the changes in proportion over time are driven by growth and the two important parameters for growth is the proliferation rate which is spatially uniform within the tissue however the other important parameters post-mytotic differentiation which removes progenitors from the pool and that is spatially varying it's temporary and spatially varying and it's a combination of spatially uniform proliferation but varying differentiation which gives you following the patterning phase explains the changes in in the proportions of domains over time Is that regulated in the machine? No I mean in a hand-waving kind of developmental genetics way we can say we know things about not signaling but in a quantitative terms no okay so the final point is thinking about gap genes and anti-parallel gradients maybe something very similar is going on since the overall topology of the gap gene network is very similar to the neural tube so let me so for the last part of this talk the decoding map section this is work from Anna Cachiva and Marcin Zagorski and it's been in collaboration with Tobias Bollinbach and Kasper Tachic at the IST thank you